I generally use the capstan to pul the boat up to the anchor unless it's windy.
A good winch in good condition should handle that in benign conditions for a very long time.
The "heads up" in this is not to use the winch to pull the anchor out of the bottom. Get right above the anchor then go back and forth gently untill the anchor breaks out. May need to resecure the rode more than once but it's a sure fire method and won't stress your winch.
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I pretty much do the same, except I usually creep up in the scope before I fire up the engine. When I'm about 2 or 3 to 1 I fire up and put a little tension on the chain when it's straight up. Let it stay like that for several seconds then idle in reverse only. That normally breaks the anchor free.