Helps you practice, study, and learn it all faster.... since you can sight read what's on the paper quickly and easily to understand the examples in theory textbooks, rather than having to have someone teach you by ear or to have enough knowledge to slowly work out what each note means in written form but not to be fast enough at it to be particularly productive.
So imho, it helps with the execution of anything theoretical to be able to sight read. Sight reading skill is a great benefit.
However, there's absolutely no REQUIREMENT for it to do what you're doing.
To put a background on my perspective: I have been able to sight read since before I could read and write the alphabet, due to how I was brought up by a music teacher. However through my career I've taught myself new instruments along the way, ones that I couldn't sight read on accurately at all. One of those, surprisingly enough, is guitar. Because I can read treble and bass clef just fine, it ought to be fine, right? And I can sight read on bass without thinking about it. But because bass and guitar are essentially played exactly the same way with same tuning, just an octave apart (ignoring the extra 2 strings for now), it completely threw me off so much that I couldn't sight read on guitar for many years of playing professionally, and I'm still slower reading on guitar than on bass by a looooong way.
My point being - I have experience both as a really good sight reader (sight reading new music classical, jazz, rock, funk, on different instruments)... and as someone playing professionally on instruments I play well but couldn't sight read on at all. In all of those situations I have had plenty of new theory learning situations, whether it was learning/mastering modes, learning increasingly obscure jazz chords and transtitions, or learning "new music" in the classical field where your previous theory knowledge gets taken to a crazy new level of mathematical complexity.
And I can definitely tell you that translating the theory into the instrument without sight reading was much harder for me to get into my head.