Yes, the tumbler AND the old key both wear over time, so if the new key, which is cut "correctly" by MB, doesn't work well, then the tumbler is worn out too, and should be replaced. If you just continue using the old key, it won't get better, it will only get worse, and you DON'T want to deal with a stuck tumbler. Big pain, big $$$. I put up with mine sticking for a long time, and got burned because one day it wouldn't turn from the off position and I had to drill it out!
If I had not put it off, it would have been MUCH easier to deal with.
Mike