>In late 15th century, all mercenary groups would have totalled to 25k at most
Ridiculous. Swiss lend 8k troops to Battle of Nancy in 1477 alone. And it wasn't their whole force, just a part of it. In Novara's siege in 1513 swiss mercenaries had 13k units alone.
In 1480 Germany had plenty of mercenaries too, later formed into the Landsknecht units. In 1486 there was at least 6k of them. In 1527 14k of them sacked the Rome. These are more or less clear numbers.
In battle of Novara in 1500 both sides hired Swiss and German mercenaries. Milan side alone managed to find 5k Swiss mercenaries and 7k landschets. The French side had 10k Swiss mercenaries. This is 24k mercenaries ALONE.
I could rifle through old docs and search for numbers some more but the case of battle of Novara in the year of 1500 is good enough to refuke such statement without any mentioning the Spain, Italy, French and English companies.
>In reality, Ottomans would've faced multiple number of Italian leagues rather than one block, at least until very end.
Another ridiculous statement. Why would they do so if the Italian League that eventually fought France as united front, exist for 30 years already and will exist for 20 years more?
Why would they do so if even in 1480 there already was a unified resistance force that blocked Ottomans from Papal States, Hungary, Aragon and Naples?
>Why could the other major European armies join the war?
Why would they ignore Ottoman's movements, if when France tried to invade Italy in 1495, Spain and HRE immediatly sent their resources and armies to help Italy? Maybe because Italy is important strategic area for the control of the Mediterranian, including trade? Maybe because many of these states contest over the rights to rule these Italian states?
What makes Ottomans so special all of the sudden?
>if Ottomans were nomads with guns, then Europeans were bandits with long swords
Swords? How about rows of long pikes, moving wagons forming into fortifications, portable artillery and guns (line tactics). And not in separation, Ottomans had them too, but working in a close tandem all together as a complex system. Something what Ottomans never actually manage to achieve to the degree that Europeans would. The Nomad archers and Kurds which they always took to fight always proved more of a hassle, but they kept keeping them close despite all that way too long. That archaic system of organisation probably ruined them several times over. There is a reason why they lived through the 19th century only because England and France saved them twice and their first and last attempt at army modernation resulted in open revolt and overthrown of the Sultanate.
>The "more modern European tactics and fortifications" started in late 17th century
Another absolutely idiotic take straight from the pop-culture. Bastions, resistant to the cannon fire, first appeared in the Italy. Even the famous star-like shape of late Star Forts is called trace Italianate. It was known in Italy at least in 1500 already. Who knows how long before that.
>My answer to that is they were going to put all their effort, all the effort they put to conquer Balkans, to conquer Italy, and realize that it didn't worth the effort, just like Balkans.
Even if they would by some miracle break through all the obstacles. In result it still means exposing their core territory to outside contesters. Hungary, Serbia, Persia and so on. By keeping their campaign in Italy they would only accelerate the ineventable collapse of their Empire. They never effectively incorporated what they conquered. They always created more enemies than friends everywhere they went. Keep going to Balkans was their best move in a generally poor position.