I doubt that although I had confusion earlier on the other thread of BitCryptex. When we open or close channel, we do need of On Chain transaction which is increase in a significant numbers once LN gets a good adoption. You will certainly not be holding your big sum on LN for a long time.
There's exchange option for LN BTC to On Chain BTC which will increase as well. People will mostly utilize this to increase inbound
I believe the idea is to keep your savings in cold storage, and to keep your monthly expenses in a LN channel. Avoid closing that channel, only when necessary to avoid paying fees again.
And you just round your channel every month or so to pay the next month expenses.