I'm old enough to remember halfpenny coins here in the UK. I've got a few someplace that I kept.
When they were withdrawn in 1984, they were worth more than 1.5p in today's money. The country survived, so I dare say we could safely discontinue 1p (and 2p) coins.
I remember Polo mints going from 4.5p to 5p in ~1975. (I was 7 and such things were important...). It's curious that the minimum possible percentage increase then was 11%, but now, when Polo mints are around 60p, the minimum possible increase is 1.7%. Getting rid of all coins < 5p would return us to the same "granularity". (And possibly be inflationary.)
When they were withdrawn in 1984, they were worth more than 1.5p in today's money. The country survived, so I dare say we could safely discontinue 1p (and 2p) coins.