Sprocket wear is mostly, near totally, caused by worn = longer becoming chains.
The width doesn't matter.
I've run 1/8" chains on 3/32" sprockets, and since 4 years a motorcycle 1/4" chain on 1/8" sprockets.
Begin 2019 I decided to not replace the chainring when mounting a new chain (after tensioner at its end).
That chainring is still mounted, with 60 km daily cycling, and didn't wear further, with now it's third chain mounted.
Dito for the rear cog, I had 3 replaced ones with too short teeth appearing to break off easily.
I remounted them, and teeth only began to break when tensioner position was closing in on its end.
Replace the chain before it starts eating sprocket teeth to break oif and you can just keep the sprockets.
Also saved me the hassle of having to flip the sprockets upon sharkfin shaping and chain having to climb up the inner of the hook in order to disengage.
My current chainring, Velosolo, is lasting nearly 4 years. well over 70000 km and if I would replace the chain before tensioner end, the Velosolo bolt on cogs would probably too.