No, it is not a big deal to blow past the center line. It should be a part of basic training how to deal with it before you ever get your private also.
If slow traffic is in front of you, fly an extended downwind, or makes some S turns, again those types of situations should all be basic training. If you get to 45 hours and your instructor hasn't been over all of that, they are crappy at their job to say the least. Just like a missed approach should be a nothing burger. I actually ask my passengers to toss scenarios at me that make me deal with them. Yesterday set up on short final, going pretty slow because its a short airstrip to get into, my girlfriend yelled at me " Imaginary moose on the runway".