I don't have anywhere near the level of expertise necessary to make an attempt at answering your question in its present scale, but I can offer you one anecdote that might illuminate how a unit gets "worn down" almost to the point of extermination in one battle.

I did a case study of the Austro-Hungarian First Imperial-and-Royal Landwehr Regiment during their first battle of the First World War. More specifically, I focused on its II Battalion, a unit with a strength of roughly 1000 men. Going into battle for the first time on 26 August 1914 around the Polish city of Zamosc, II Battalion , with its four 250-man companies, was ordered to take a Russian defensive position stationed on a hill about a mile from their jumping-off position. The Russians' tactical defensive position was ideal, as was often the case in the opening Russian-Austrian action around Komarow. The Russians were positioned on a wishbone-shaped hill with rudimentary defensive trenches or foxholes dug in just behind the treeline on the top of the hill. With machine gun positions on both extremities, the Russians drew in the Austrian II Battalion and positively chewed them up. Without going too far into the tactical details of the Austrians at this point in the war, it's enough to say that they weren't exactly designed to avoid casualty.

The first company to reach and storm the Russian position suffered 5 dead and 55 wounded, or about 40% of its armed strength. The other company involved in the initial charge also suffered about the same. The two reserve companies which had been sent in subsequently each took 15% casualties. With the battalion being tasked with two more frontal assault operations during the next two days, the battalion had lost a full 60% of its armed strength as casualties in the first three days of combat alone.

The battalion wasn't completely wiped out, like in the situations you're asking about, but they were bled almost to the point of inoperability. Though the entire battalion was not killed, the unit ceased to exist operationally for long periods of time, as men got separated, fled the battlefield, or were integrated into other units in the reigning confusion. II Battalion's commander, on the night of the 27th, went back to their initial jumping-off point to rendezvous with his regimental commander, only to have the regimental commander point blank refuse to believe his men were still holding the hill they'd taken during the preceeding day. So many men from the unit had been killed or had streamed rearward in retreat or with wounds, that the commander had assumed the unit to have been destroyed altogether.

Again, I know this won't answer your full question, but you can see from this one infantry assault, that it's definitely not outside the realm of reason that entire units could be physically destroyed in a matter of hours or days. And this particular battle did not even really feature the Russian artillery which was to wreak so much havoc on the Austrian infantrymen during the opening campaign of 1914. In an operational sense, units were destroyed an reconstituted even several times within a single battle, as their component units went missing, retreated without orders or simply lost contact with their commanding officers.

Sources:

Archival research done at the Austrian War Archives, Vienna, Summer 2014.

Wawro, Geoffrey. A Mad Catastrophe: The Outbreak of World War I and the Collapse of the Habsburg Empire. Basic Books, 2014.

You have to understand how warfare has evolved over time, as well as laws of war, the weapons, as well as how casualties were taken care of both on and off the battlefield.

Casualties can refer not only to those killed in action but those wounded in action. Even if a man is only slightly wounded he is considered a casualty because he has to be taken out of the unit for a short time to be treated for his wounds, thus taking the unit down a man and affecting combat capability of the unit as a whole.

30 men killed a minute in the American Civil War does sound quite terrible, but consider some of the battles of the First World War. The BEF (British Expeditionary Force) during the first day of the battle of the Somme had over 19,000 killed. In one day. The total losses for the British were over 57,000 just for that day alone. So you can see that not only is loss of life in a short time during war possible, but has become all too common.

So yes it is possible for an entire unit to be "wiped out" due to casualties sustained on the battlefield. A unit that sustained a high degree of casualties could be deemed combat ineffective and disbanded, with the remainders melded into other units. If you are wondering if that means the entire unit was killed without any survivors, it has happened yes but has become less common due to advances in combat tactics, technology, training, and modes of warfare.