By repeaters I guess you mean lever action style rifles? These rifles were just marginally faster than a soldier with a bolt action. The main issue though is that most repeaters are tube fed and if you look at how it’s reloaded it’s quite awkward. Bolt action rifles could be reloaded with 5 round stripped clips very quickly, so while the action for repeaters may have been a little faster, the faster reloading speed of the bolt action rifle gave it an edge. Another side effect of the tube magazine design was that the bullets are placed behind each other rather than on top of each other like in regular magazines. There was a fear that a sudden jolt could make a chain detonation when the tip of a bullet would strike the primer of the bullet in front of it causing it to fire. Therefore repeater bullets were typically flat nosed rather than pointed like in other rifles and less aerodynamic. Also then repeater is more awkward to fire in the prone position more mechanically complicated to produce.

The Russians actually did import repeating rifles from the US with magazines in WWI since they were so short on rifles. So several hundred thousand of these went to Russia and were apparently well liked. However in Terms of the millions of rifles they used it was a drop in the bucket.

Repeaters were in use - every belligerent in the war had a magazine-fed breech-loading rifle, which is the definition of a repeater. If you're referring to lever action rifles, there's a few reasons that relate to technology and doctrine.

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First I'll touch on the lever-action rifles people traditionally think of, like the Winchester 1894. These designs were chambered in weaker cartridges than the standard military rifles of the day, and this loss of power wasn't acceptable to commanders at the time. Armies of the time wanted cartridges capable of hitting targets several hundred yards away and with enough power to be used for more indirect fire by machineguns, and these traditional designs were limited by their design to much weaker cartridges that lacked that performance. The tube magazines were another issue, as they could only be single-loaded and weren't capable of accepting rapid-feeding devices like stripper clips or en-bloc clips. Tube magazines were a major issue in rifle trials across the world leading up to WW1 - France was the only nation to adopt a tube-magazine rifle, largely due to their rush to adopt a modern rifle ahead of the rest of the world, and several nations would suffer magazine detonations in trials that would lead to them specifically discounting tube magazine rifles.

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That's not to say that these issues weren't something that couldn't be solved. Savage and Winchester both would develop stronger lever action designs capable of withstanding full-power cartridges, and they'd both include box magazine designs that - at least on paper - made them on par with contemporary military rifles. Both these designs, which would become the Savage and Winchester Models 1899 and 1895, respectively, would be submitted to various trials in the US (both Army and New York State Militia), even seeing limited adoption in New York. The problem here was their late appearance - by the time the designs were really finalized in 1895, every major power had already adopted a bolt-action rifle.

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Now, despite all these factors coming into play to prevent the adoption of a lever-action as a standard repeating rifle, there was some limited use of lever-actions in WW1. The British Royal Flying Corps acquired a small number of Winchester 1886 rifles in .45-90 caliber and even went as far as developing a special incendiary bullet for the guns to fight Zeppelins. Larger orders were placed for the Admiralty for Winchester 1892s in .44-40 (21,000 total rifles) and 1894s in .30-30 (2,000 total rifles), with the intention of freeing up Enfields on ships and in other secondary roles. A similar thing happened with the Savage 1899, being procured by the Montreal Home Guard to free up Ross Rifles for Canada to send to their troops in the trenches.

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The real significant contract, however, was the Russian 1895 contract. Early in the war, Russia found itself desperately short of rifles, and Winchester was one of a number of sources they turned to for rifles (in addition to contracting Westinghouse and Remmington for Mosin-Nagants and procuring Type 30 Arisaka rifles from Japan). Winchester modified their 1895 design with a handguard and bayonet, chambered it in Russian the 7.62x54r cartridge, and added stripper clip guides to accept Mosin Nagant stripper clips. 300,000 of these rifles were ordered in two contracts (100,000 and 200,000), and they made it to Russia in significant numbers. Exact dispositions are unknown, but Baltic battalions - particularly Latvians - were given the rifles in significant numbers. They'd remain in use through Russia's exit from the war and into the Russian Civil War, being placed in storage following the Civil War. Some 9,000 of these rifles would end up in Spain two and a half decades later as aid to the Spanish Republican Government.

I thought I'd cover semi-automatics in WW1 military use-

Some semi automatic rifles saw limited use in the various Air services earlier in the conflict, before interrupter gear allowing machineguns to fire through rotors was implemented. In air combat the more intensive maintenance and more open/exposed parts of a semi-automatic rifle was not as much of an issue as it was in the trenches on the ground. Examples of rifles that saw limited use in Air services but not ground forces included the Winchester 1907 and the Mexican Mondragon, which was issued in very small numbers (less than 400) to the Mexican Army just before the war and another 1,000 were purchased by German air forces in 1915 and modified with 30 round magazines and issued to aircrews.

'The rigours of wartime service were not kind to the fragile Mondragon, so they were rather quickly withdrawn from frontline service... the sheer cost of a semi-automatic weapon compared to a bolt action rifle, especially in moments of wartime emergency, meant that semi-automatic rifles were an expensive diversion.' (1)

The often pistol or intermediate calibre rounds used by many of the Air service rifles were just fine for fighting against wooden and canvas aircraft, where the short exposure time for taking shots meant that more rounds in the air was better for hit chances than less but unnecessarily powerful bolt action rifle rounds from insert nation's here's standard rifle.

Assault troops, particularly later in the war did pursue weapons other than the standard rifles, but often just used shortened carbine length variants of the bolt action rifles, pistols and revolvers or simply massed hand grenades instead, as all of those weapons were already in inventories and did not need specialised ammunition or maintenance gear like many of the semi-automatic rifles and carbines used by the Air services.

Generally assault troops rather than move towards specialised infantry rifles instead saw the massed introduction of machineguns like the Lewis, Chauchat and MMG's like the MG08-15, which were used for bounding fire and for moving machineguns forwards of the allied trenches without the weight and time required to set up the heavy machineguns- Such light machineguns were seen among the Entent forces as better value than semi-automatic infantry rifles. (2)

Assault troops using converted pistols is also where weapons like ones the Luger Lange PO8 Luger and it's carbine variants were popular, as trench raids could take existing, in-inventory weapons and ammunition and add stocks and extended magazines (as well as experiments with both fully automatic versions of the Luger and C96 Mauser (3) to have effective trench weapons without the logistical strain of completely new weapons. (4) Other nations also often equipped raiders with pistols or revolvers, an example I’ve seen a photo of was French trench raiders circa 1916 during the Verdun Campaign armed with revolvers and satchels slung on their sides filled with up at or more than a dozen hand grenades instead of carrying a regular rifle or even shorter carbines.

American use of shotguns after their own deployment to mainland Europe was highly exaggerated by the American press for their own propaganda purposes as being a unique advantage of Americans. In reality despite their fame the vast majority of shotguns, even ‘Trench’ models, were used for rear-line actions such as guarding railway lines and particularly prisoner of war camps. Less than 2,500 of any model shotgun was actually ever issued to units near the frontline, including shotguns like the Model 10 and M1897 ‘Trench Gun’, which was never referred to as such in official documents, only by the press and post-war works (5)

Many trench raids on both sides were prepared for the night before, with the attackers crawling over No-Mans land in order to reach a forward staging position. These teams would then set up light mortars or machine guns in hidden positions during the later periods of the night, to be used during the later assault in the pre-dawn or early morning.

I know that for the Germans the Madsen Light Machinegun was very highly prized in this role due to it being much lighter and easier to move into these forward support positions but they were in low supply, so the MG08-15 was a stop-gap developed later in the war that was much heavier and more cumbersome to move forwards, but used existing parts and once emplaced was a powerful support weapon. The French used the lighter Chauchat in a similar role to the Madsen, but they had much greater numbers of the teams.

The popularity of the Luger among German and Austrian stormtroopers/ trench assault troops in particular saw the MP-18, the first combat used and generally reliable and modern in concept sub-machinegun, use Luger based drum magazines due to them being in use already rather than the originally planned stick magazines, something that would come back in the later post-war variants of the weapon. (6) (7)

The biggest standout among the rifles would be the French RSC 1917, a semi-automatic rifle that was indeed designed for infantry use, and saw combat on the ground rather than as an an Air rifle. This rifle was mass produced, but due to it being more complex than regular french bolt-action rifles like the Lebel and the Berthier, was often issued out as a kind of designated marksman rifle, to the most accurate shooter in the platoon, rather than as a full standard infantry rifle.

(1) Chris McNab, German Automatic Rifles 1941-1945, preface on earlier semi-automatic rifles.

(2) Robert Bruce, Machine Guns of World War I

(3) Darren Weaver, Mauser Pistolen: Development and Production, 1877-1946 , 2008

(4) George Chin, The Machine Gun, Vol. 1: History Evolution and Development of Manual, Automatic, and Airborne Repeating Weapons, 1951

(5) Bruce Canfield, Complete Guide to United States Military Combat Shotguns

(6) Joachim Gortz, Geoffrey Sturgess, The Borchardt & Luger Automatic Pistols , 2012

(7) Luc Guillou, German Submachineguns, 1918-1945, 2018