Life savings on lightning netwerk?

Now we all like to keep our btc on a hardware wallet, but how does that work in a world with the bitcoin standard?

I know lightning will take over all the small payments but what about your salary?

I assume the transaction fees will rise and only the important transactions like opening/closing lightning channels or big payments will be on the blockchain.

So when people get paid, where does your money go? If everybody's salary needs to transfer over the btc blockchain will the fees rise to much or is there plenty of space?