How important was physical strength in premodern warfare and how did it affect militaries?

In premodern warfare, I would say that strength was incredibly important for one major difference between modern and premodern fighting: marching.

The modern warrior of the 21st century can most likely rely on automotive transport, whether by land, sea or air, to reach the battlefield and move to and from where he is needed in a timely and most strategically advantageous manner.

Even lacking engine powered transport, they would still at least be able to resort to bicycles which while not perfect were certainly an improvement only travel by foot.

In the premodern era, the arguably speediest form of travel would have been by boat.

This has the added benefit of being a vehicle so the troops would not tire as they would from marching.

But this might not have been possible for various reasons, particularly for a whole army. They might be too far from the ocean or their destination in the other direction. The season might be too dangerous. There might not be enough boats or supplies to last throughout the voyage. Malnutrition and disease.

The next best thing would be horses.

But horses tire, require feed and care, were and still are quite expensive to buy/raise and maintain.

Also, as much as many movies and books might lead one to believe otherwise, even if an entire army did have the option to mount every single one of its soldiers, they would not cover much more ground than if they were on foot!

This is due to various reasons. Firstly, while a horse at full gallop is indeed very impressive, unless it's some cyborg beast from the future, horses cannot keep up a very strong and fast pace for very long. They would literally die from the exhaustion, especially if forced to carry a fat human and his gear along for the ride.

Then there's the possibility of the horse hurting itself. Maiming a horse is as good as killing it, even today with advanced medicine. If a horse breaks its leg tripping or getting its hoof caught on something, chances are it will be put down. So to avoid such dangers, great care was taken to keep to clear and solid roads.

Which brings up another point, almost everything traveled faster by road, including horses. Rough terrain would slow down a horse. They are not unicrorns that can leap across hilly ground.

Carts and wagons are naturally drawn by horses or oxen during premodern times so those aren't an option for moving an army.

So we are left with marching. This is the general's best bet for moving soldiers to and from battlefields in a reliable, timely and strategic manner.

This is probably the number one reason why strength (and general health) was incredibly important for a soldier. Nevermind not having the strength to hold a spear or sword. If an army was too weak to march for weeks at a time, they would never even arrive in time for the battle. Or worse, the battle would come find them, likely at a poor time.

While body strength is still focused on a great deal in modern military forces, it's not nearly as essential as it was in the old days.

Back then, if a soldier lacked strength, he was essentially useless as a soldier. He would slow down an army on the march, could catch (and thus spread) illness, and would be a liability in a fight, whether he used a spear, sword, axe, or bow (since all these weapons require repeated application of force to be used properly).

Now a days, you could theoretically be severely ill with dysentery, have lost use of some choice limbs, and be unfit for travel on foot and yet still fight, albeit far from ideal. Though if soldiers in such a state had to fight in modern day, their situation is probably terribly grim.

Hope this gave you something to think about! Cheers!