COUNTER=$((COUNTER+1))
is quite a clumsy construct in modern programming.
(( COUNTER++ ))
looks more "modern". You can also use
let COUNTER++
if you think that improves readability. Sometimes, Bash gives too many ways of doing things - Perl philosophy I suppose - when perhaps the Python "there is only one right way to do it" might be more appropriate. That's a debatable statement if ever there was one! Anyway, I would suggest the aim (in this case) is not just to increment a variable but (general rule) to also write code that someone else can understand and support. Conformity goes a long way to achieving that.
HTH