This is just not the case in most software engineering jobs outside things like startups where you're on the original team, or your pet project.
In a team amongst other teams, you'll be reading code that you need to integrate with, reading colleagues' code when reviewing, and generally be producing much less than the sum of the code produced by everyone else on your team and your dependencies.
If you're the single owner of a component or subsystem, then it can be true, but that's not normally healthy for a software company - it implies a low bus factor.
Your typical company has a bus factor of 0, having one programmer who knows the code seems like a huge improvement over that.
I did find that I was able to use my code writing skills to bootstrap the code reading skills. If there was code that struck me as obtuse, I would try to refactor it. Sometimes I found that the code really could be written more simply. Othertimes I found that I had missed something important about what was going on. As I did this, I learned to better intuit what the original authors probably meant and where to look for confirmation/rebuttal.
Code reviews can only enforce existing practices and style, rethinking architecture is a different matter.
For example, should a new grad be able to read your code without help? Should a 5 year old? At some point, you are spending more time writing design docs, refactoring the code, simplifying the tests, and gathering learning resources than you are just writing code that works.
Newer engineers rarely hear about how much they need to learn to read good code, and how much disagreement there is about what good code looks like. As a result it is easy to get into the mindset that "surprising" or "complex" code is bad. Instead, it would be a lot better if engineers are encouraged from the start to see reading code as a challenge. Nobody starts off knowing grep, folder organization conventions, go-to-definition shortcuts, and architectural design patterns needed to understand certain pieces of code.
To improve yourself, you are better off focusing on writing code, but at the organizational level, it's better for the team if people are willing to assume that reading code and writing readable code aren't an easy tasks.
I think this is probably more true for you than it is for us corporate schlubs :)
For those of us with less talent at writing a unique piece of code, the process of diving in and figuring out a mess is actually a learned skill that we get better at over time, possibly the most important one.