I prefer them to go for LN rather than main chain transactions, or both. I find it increasingly less appealing to see merchants jump on board with the fees being too high for most people to be comfortable using it.
It's pointless to do some low value grocery shopping when you pay a buck or two in fees, especially with how speculators bump the fees by using higher fees to front run other people's transactions.
It may sound a bit harsh, but that's just how the reality is. Fiat payment options or just cash work better for in-store payments and are cheaper than main chain transactions. Innovation is accepting LN, especially for a supermarket.
What fees are you talking about, are you talking about those companies which are responsible for pos transcations?
I am wondering how much time it takes to make such transactions by register, because sometimes btc txs takes a while and it wont be logical to make those by register.