Lots of short drives means more time spent with engine & oil cold, which can increase wear but wouldn't be fixed by frequent oil changes.
It could also mean more blowby and less time to boil off water & gas in the crankcase. More frequent oil changes might mitigate this, but I suspect it's minimal...you're probably still getting warmed up enough to get rid of most of it, and if you're not and it's accumulating drive after drive, an early oil change is only going to fix it temporarily.
But an oil analysis should be able to tell you if there's an issue or give you peace of mind. You could take a sample at 3000 miles without changing oil, and then again at 6000 with an oil change, and include it in the notes to see what they think.