Computing theory is only going to make you "way better" if you're doing lower-level stuff. It'll still make you somewhat better with high-level languages, but those languages (and optimizations at the compiler level) will abstract the really complex theory away. Understanding memory is really important, though.
In general, the thing that's made me a way better programmer is seeing how highly experienced programmers explain the way they organize their code. Even though I don't practice functional programming, reading the reasoning behind it has been really helpful to me, and there are many principles from FP that make object-oriented code far better.
> I've built complex systems and user interfaces, but I couldn't tell you about quick-sort algorithms, or sieves, or the best way to build a fibonacci sequence; I wonder if my programming is objectively worse because of it.
It depends on what you're doing. For the vast majority of people, especially those in the business world, the answer would be "no". Many of those parts of programming (sorting, linked lists, random number generation, etc.) are provided by standard libraries or other programmers. You don't want to constantly reinvent the wheel if someone is paying for your time.
If it's something like cryptography, it's a lot murkier of an issue. It's really hard to evaluate a crypto package if you're not an expert, and even the "industry-standard" packages are often found to have holes in them. I'm still not suggesting you write your own, but it's always worthwhile to understand data security better.