The problem as you've stated it compares replacing an AA battery (necessary very often) to replacing a rechargeable battery (only necessary when it's health depletes after years), so your characterisation of it so far is unreasonable, which is why I asked again.
If it's both you've failed to explain any inherent problem with non-AA batteries when it comes to the time taken to change them. I can change a the custom battery in my camera as quickly as any AA. Faster, even, than the typical AA sprung enclosure because of the housing.