Smaller cogs wear out themselves and chains more rapidly since they share the load over fewer teeth and the chain has to make a more severe bend to go around them. So using larger cogs and shifting among them does make the cassette last longer and the more gentle wrap makes chains last longer too.

Single speed/IGH setups tend to use moderate to larger cogs and chainrings ( no 11 or 12T cogs for example) and the chain runs in a completely straight line (assuming proper set up) so there are no side loads.