Very well put. I'll have to give this some thought. I don't want to return to the days of crazy bonuses to everything, but you have a good point. To me a lot of this stems from the idea that your ability score modifier can represent some training while proficiency is there for addition training and practice, etc. I agree that some skills simply don't work if you don't have training in them.The basic premise behind Bounded Accuracy is that anyone can attempt any task, and a bonus can only help you. (As contrasted with 3E, where you had a minimum bonus required before you could even participate.)
The fundamental flaw behind Bounded Accuracy is that a world where anyone can do anything would be silly. As an example, consider the manacles in the equipment section, which require a DC 20 check to slip or break. What good would manacles be if anyone with at-least-average Strength or Dexterity could escape them? The average person should have significantly less than 5% chance of escaping manacles, or else nobody would bother with them. Really, you should need significantly above-average ability in order to defeat them, if anyone is to consider them reliable enough to use. My chance of slipping manacles, or climbing a wall, or crafting a sword, really should be zero; I would need significant training before I could even begin to try.
The other major issue with Bounded Accuracy is that you can't represent the most common types of tasks - the ones that would be routine for a qualified person, but nearly impossible for an unqualified one. When it comes to picking a lock or identifying a spell or playing an instrument, you should have very close to a 100% chance of succeeding if you know what you're doing, and very close to a 0% chance of succeeding if you don't know what you're doing. If you know how to play the flute at all, then you should be able to play the simplest possible song (whether that's DC 5 or DC 10) whenever you try; but minimal training is only a +2 bonus, so even if you have an 85% chance of success, then someone who has never learned how to play the flute is still guaranteed a 75% chance of success. (Which is ridiculous.)
The difference between trained an untrained should be somewhere in the +10 to +20 range, in order for the world to make sense at all, but that's fundamentally at odds with the concept of Bounded Accuracy.