Not in "real time": blockchain settlement has to wait for a block. And you incur on-network transaction fees plus whatever fee the exchange imposes for transfers out.

(Besides, many people are "day trading" on these exchanges because it's a form of addictive gambling)

Oh and then there's "staking": https://ftx.com/staking which encourages people to keep tokens on the exchange by pretending to pay them interest rates. And offering various other multi-level-marketing incentives. I see "Free Daily ERC20/ETH Withdrawals : NaN" on that page, which is fun.

You can, but it's impractical (operationally and in tx costs) as it requires a live bot to constantly adjust margin between the exchange and the self-custody wallet, due to the way typical crypto trading products work: at max margin, the chance of liquidation is too high, not so much because of liquidation itself (that can be risk managed and averaged out) but due to the enormous implied fees associated with liquidations. Example pricing: bet 5 at max leverage, lose 2 due to market movements, the account is zeroed aka liquidation fee of 3.

Actually using crypto is ridiculously complicated compared to a SEPA transfer from your bank account or a shares trade in an app.

People like the path of least resistance which is why everyone uses exchanges- it's easier than using your own cold wallet. Exchanges for good or ill has made crypto accessible to the masses.