The fact that it is healing makes it hard to fully see how it's going to look...and you are correct that no tattoo is perfect and we all tend to over -scrutinize our own work. But, if this was mine, I would not be at all happy with the work being done. I would definitely be looking for someone who might be able to either save or cover the work.
Of course, there are other more experienced folks here who can chime in, as well.
Only you know what's possible with the artist. The bottom line is this is your body - art you will wear forever. Personally, I would be looking for another artist/shop.