Isn't Lightning solving this problem? Plebs using Lightning for small transactions? It's happening already.
Discussion
No, the small lighting transactions are not actually ''real'' lightning transactions, but besides that it will always boil down to your ability to close a channel; which is an onchain transaction. Lightning does not reduce that threshold of onchain fee's, but it allows you to distribute those costs over many interactions.
Note, i use lighting (and for small tx's), all the time, to get a shorttime vpn or silly AI pictures.
Well if you run LN node then you care about channels and closing/opening them but you can use Lightning without those things and simply enjoy fast network with minimal fees.