Yes, but setting aside direct ownership which is not a prerequisite for investing in any coin, how is bitcoin a better choice? It seems to me that is like saying, well you really should have invested in Exxon and you would be ok now.
Blockchains like Ethereum are not (and aren't meant to be) alternatives to fiat. In fact, the best thing for ETH would be low price, since it's mostly used as gas. Altcoins are almost entirely vaporware until ETH tech matures and consumer services become feasible. Until then, any high valuation of either ETH or Altcoin is 100% Tulip Mania. I have no idea about any blockchains outside of Bitcoin or Ethereum.
"Not your wallet not your coin", or whatever they like saying, is just is just deflection from valid criticism that crypto is very easy to exploit without recourse.
People are learning to use better passwords, and people learned long ago to keep their paper money in a wallet. The same will happen with crypto.
What’s the motivation for this to happen?
It depends on a lot of factors; like how important it might become for people to avoid using fiat or government controlled digital currencies, or how deeply integrated it could become in daily life.