There nothing wrong in having bikes. We have 15 between the two of us. Some get ridden regularly, others are back-up bikes, and others are future restoration projects. And we plan on getting more.
As to appearance, there is nothing wrong, either, with having a bike like that one. You should have seen the old MTB that I retrieved from a rubbish dump that served as my commuter bike for four or five years. It's gone back to the rubbish dump, but it served me very well, and always looked like it was on its last legs.
Fenders? They were put on there for fun, keep them on there for fun. They make the bike even quirkier, and we can't have enough quirky bikes out there.