Is it bad to turn the engine on and off frequently

[oj88]

weaker batteries won't expedite the death of starter motors.
on the contrary, starters will last longer, because they won't function because the battery ain't got no juice to make 'em function.

I think what he meant was, with a weak battery, it may not have enough power to even turn the starter so it ends up burning the starter winding. It’s the same reason low coltage (ie. 110v) will kill your unprotected 220v appliances that uses a motor (ie. Old school ref and A/C).

On the topic, you can’t cheat physics. Frequent start-stops will definitely put a toll on the battery, starter, and related parts. By how much, will depend on the quality, tolerances, and design of the individual components. Internal to the manufacturer, these components all have MTBF and duty cycle figures which are not typically available to the public. The best thing to do is to use good judgment to balance between protecting the environment vs your vehicle and do the start-stop dance only when absolutely necessary.