when blocks remain small, lightning can't scale without custodians. even if every single transaction on L1 was dedicated to maintaining lightning channels, it would still top out at a certain number of sovereign users, and to get more converts to the bitcoin religion you would need them to use custodians. why are you okay with that? do you really think it's cool that someone else can just steal your money or rug you? are you really cool with only a small percentage of the wealthiest bitcoiners being able to own their own money, while everyone else has no protection from getting robbed?
Nobody is going to spend from a cold storage wallet in regular transactions. It is reasonable to expect people to transfer from cold storage to a more capable hot wallet.
Block size does not matter. LN can support millions of transactions a second.