So it's not really different if you hold the BTC (improductively) in your wallet.
Strongly disagree ! You are leaving your coins in a hot wallet on alpha software (and protocol!) here.
So it *is* different, just a trade-off (that a lot of us choose to make, at least for part of their funds).
Yes, here you're totally right, security wise it is more risky. But most will choose to not exactly the funds that they would hold alternatively in a cold wallet, but a relatively small part.
If only 2% of all Bitcoin hodlers (estimated at 25 million worldwide,
e.g. here) would participate with 2% of their funds, LN liquidity would see a massive boost already. Currently we have only about
33-35K LN nodes and ~1100 BTC capacity. The "2% of 2% scenario" would make LN grow to 500K nodes and to a capacity of 0.02 * 0.02 * 20 million = 8000 BTC.