Why would the "tower" have any interest in whether you're stable or not?
The notion of being "stable" on finals is surely a relatively recent fly-by-numbers sop concept developed by some airlines' Operations and Training depts and has absolutely nothing to do with ATC; 10 years and more ago it had hardly if ever been heard of - anywhere.
Has it somehow transferred to puddlejumpers now? For what purpose? Energy management is hardly the critical feature there that it is in a 737 or larger, is it?
I can think of reasons why s turns on finals may not be a good idea but "stable" wouldn't be one of them.