Jomini,
I generally agree with your points about a professional army. It would be great to have this simulated in EU IV instead of the lame "units".
The Ottoman system was not pure rule of the strongest, though. It was the strongest of the ruling dynasty. In the Central Asian tradition only the descendants of Genghis Khan or Oguz Khan can be a Khan. However, the Janissaries were closer to 5000 before 1450 (10k refers to Mehmed II era), and could be kept under control relatively easily. This doesn't mean that they did not cause any problems. Bayezid (at his succession), Mehmed I and Bayezid II all gave them concessions. Indeed Bayezid II's reign was peaceful partially because the Janissaries (and other military classes) didn't want another ruthless campaigner.
About the siege of Constantinople, contemporary records agree that the cannon fire brought down the walls. Cannon fire by itself was not enough, Jannisaries alone were not enough either, but both were important. About mining and tunneling, remember what you wrote before, Constantinople was huge. Mining the wall will collapse a section and any housing adjacent to it, but it would be nothing compared to the size of the city. That also means you don't have to concentrate your army in a small area. You can spread them out unless you are ready for an assault and reduce the chance of an epidemic. As to navies, "the enemy" was the ERE, not the Italians. And yes, Bayezid I could have built a navy allied with an Italian state or the Mamluks. Bayezid II did neither, he did it with Ragusan help.
About Varna and Kosovo battles, I don't have the Aşıkpaşazade text, but I have a modernised version of Neshri. He describes the Kosovo battle in more epic terms than Varna. No mention of the army sizes, except he writes that 80-90 thousand heathens were killed in Kosovo (and only 150 Muslims!). He calls it the greatest victory of Murad, but according to him Varna was more closely fought (he writes that Murad wanted to run away at some point). Frankly speaking I am not particularly interested in the details (e.g. where the Polish charge was stopped) and tactics of battles, I am more interested larger strategy, diplomacy, logistics etc. My point was (and still is) that it was as likely that Ottomans win in Ankara or in Belgrade, as they lose in Varna or Kosovo. Also, in all of Ottoman history only one Sultan died on the battlefield, even though the Sultans fought a thousand battles. That was not luck. Even if they lost in Kosovo (already a "what if"), it was extremely unlikely that both Murad and Mehmed would get killed. At that level of "what if" you can as well land Aztecs in Europe.
Nonsense. In a period of high disease the house of Osman had precisely 0 rulers die of disease or battle with no heir. This was defying the odds - the French, English, Burgundians, Marinids, and dozens of other states all had significant power vacuums form in this time frame when lack of heirs became a problem ... and they didn't kill off all the spares. Yes, I know Turkish hygiene was superior to Western Europeans ... but the fact of the matter is statistically speaking there should have been a major crisis at least once in the 1400-1500 timeframe due to actuarial death of the Sultan with a minor heir. Now somebody has to luck out and beat actuarial odds to counterbalance the poor guys who do worse, but the Ottomans were never pressed with a major power vacuum due to untimely death of the sole survivor.
Main disagreement is the one about Ottoman institutions, you think they were fragile, but history proves you wrong, as the Ottomans and their institutions survived all kinds of crises including numerous civil wars in the 15th century. I also don't know why you think the Ottomans never lost heirs to disease or battles or had a crisis. They did. But they survived it because they had a robust system.
Let me explain in detail. In the 15th century, a normal Christian ruler married a noble woman (no divorce) and produced a few male heirs. An Ottoman ruler married up to four women (plus divorce, plus concubines) and produced at least five male heirs. When a heir died in childhood due to primitive conditions back then it was a major problem, for the Ottomans, it was less of a problem. They also had better hygene as you wrote. Even genetics played a role after the 15th century because the Ottomans did not inbreed unlike other nobility. To the contrary, they reproduced with the healthiest and smartest concubines they could find. The results were pretty random, of course. For me the best argument against eugenics is the fact that inbred Charles V and his cousin produced Phillip the Prudent, while Suleiman and Hürrem produced Selim the Sot...
As to death from battles, unlike some other nobility most Ottoman rulers did not charge into battle unless they had to. Probably another aspect that comes from the Steppes. Only one died in battle (due to trickery by most accounts), and his son (who did things like charging into battle) got captured on another occasion. Compare that to the number of rulers killed and captured by the Ottomans in battles... Ottomans did not charge into the enemy Household Guard for glory, like the Polish King did in Varna just before he got beheaded.
Ottoman heirs received an excellent education after Murad I, and had experience as rulers as teenagers in selected provinces. They had wives and children as soon as possible, even before ascending to the throne. The favourite heir was helped by the establishment to ascend after the death of the Sultan. Once he reached the capital and took control of the Janissaries, the brothers had little power to do anything about it.
Let's prove the points with a case study. Mehmed II, the Conqueror was the THIRD son of Murad II. He also had three younger brothers. Murad's eldest son and heir died after falling off the horse or some "stupid reason" like that. The second one died in childhood due to disease. Murad II was so depressed he abdicated the throne (probably the only time in Ottoman history) and left the 12 year old Mehmed II on the throne. A child on the throne was one of the reasons behind the Varna Crusade. But the child was already a leader. He spoke many languages and had studied the classics. When the Crusade started, he famously wrote his father "If you are the Sultan come and lead your army, if I am the Sultan I hereby order you to come and lead my armies". Mehmed II fought in countless battles but didn't die or got captured by the enemy, but that was not because he was a coward. In the siege of Belgrade he fought personally to prevent a total rout of his army and got wounded in the head. Yet he died of illness (or got poisoned) at the beginning of a major campaign. When he died his favourite son lost the throne and there was a crisis but it did not stop the rise of the Ottomans, even though Bayezid II undid some of his work.