In other words, if there were no central brokerages and all investors of Bitcoin were forced to mess around with private keys
If by "investors" you mean everyday laymen who wanna make a quick buck and saw a "Binance" ad in YouTube, then yes. But, if you don't, then I think you underestimate serious investors. I believe every serious investor in Bitcoin is capable of protecting a seed phrase. Not only that, but I believe they are aware of what happens to their money if the central broker goes out of business.
Speaking out of experience with my interaction with serious investors, they don't invest into stuff they don't understand. Buying bitcoin and keeping it in an centralized exchange means you don't understand it.
Unless we're talking about the cash in your wallet, most people want to keep their holdings in their name.
Sure, but you can't keep bitcoin in your name, whether you like it or not.