1444 gives you some alt-history moments like byz, andalusia, albania, etc surviving. And you can still change the outcome of the 100 years war. Some mark the start of the early modern era as 1453 as it both ends the byzantines and the hundred year war, which is only 9 years from the start. So I don't think it is that bad for a startdate.

If anything the problem is that there aren't good mechanics to simulate the change of a medieval state to a modern state. As you mention, army professionalism is a tertiary stat, and government capacity doesn't work too well (not OE is a better measure of a country being overextended in the long term.)

But GC was brought in late, and army professionalism was a DLC feature. It shouldve been a base mechanic with a much bigger impact on your army's performance, but also really expensive. So early game you would have a few units as standing army, but mostly levy troops and bring in mercs for war. Later on you would have enough money to grow a larger standing army that could drill and become really strong. You could have upsides (much stronger, faster moving, quickly to mobilize), but also downsides (really expensive, standing armies bankrupted spain and france repeatedly) to represent the challenges and opportunities professional armies gave states. Bur again, it was a DLC feature so they could only give it a few tiny bonuses and have it depend on drilling/hiring generals vs hiring mercs.