What matters is how you handle that feeling. If you run with it and continue to operate as though the code is terrible, you're probably not going to get very far as a developer. If instead you take a step back, work to understand the code, and think about what led the original author to make certain decisions, you'll do quite well.
I get what you mean though. I've seen dreadful results of some people who tried to replace a WinForms app with a WPF app and the people who did the WPF version totally half-baked their underlying framework. It was very amateurish. In contrast the existing framework built on WinForms was 90% baked. It simply had a lifecycle the developer had to understand (very difficult, nobody got it right) and was essentially only missing a final inversion of control layer to tie it all together. I added the missing layer and time to implement a new screen and number of bugs plummeted.
I thought it was crazy in 10 years of that code existing and hundreds of people having worked on it that _I_ was the one to spot that and go "hmm, you missed a spot" and have such a dramatic impact with a single week of work.
It still fucks with me to this day that _nobody_ was either capable or willing. That just blows my mind. It stuck out like a sore thumb to me. It seems to be the pattern thats emerging in my career though. I've come to understand it's a rare thing. So, fundamentally I agree with you're advice as it applies to most people. I just know first hand there are some people out there that understand exactly how to breathe new life into old systems and how to prevent new systems from decaying.
Sometimes it's cheaper for a business to rewrite something (the size of that something is highly context sensitive), than it is to work around a poor approach to a problem.
I know we love to believe in the industry that everyone is a genius and any self-doubt is imposter syndrome, but as Camille Fournier put it: "This is Hallmark card pablum".[0]
[0]: https://twitter.com/skamille/status/1004735128726376448
If you have more experience in the problem domain (either business or technical), then you might actually be able to rewrite it much better. But then there are quite a few other problems: Do we have time to rewrite it? Will it integrate well? Are you actually solving the right problem? Is it so different people won't know how to use or maintain it? etc.
I think even if you're rewriting code, doing it in the framework that's already available, and making as much use of it as is reasonable, is the better option.
I don't think it really matters what the solution is, within reason, as long as everyone agrees to follow it.
I once worked a contract where it was expressly forbidden by the dev manager to refactor any code unless it was demonstrably necessary to support a new feature. Not much fun for devs at times but I respect the reasons behind the decision (esp. as it was a derivatives trading platfom and it can get pretty expensive pretty quickly when they go wrong).
In a business setting all decisions should come from a business analysis, not from an inner desire for beauty.
Beauty is important, but save it's search outside business hours.
I'll take this one step further and say: if you think this, you're unqualified for the position. You are an amateur.