> But, I don't know that it's ever truly helped me move faster
It's incredibly helpful to move fast on large projects.
It's not about missing null checks and other simple things. If you change code in one place, that happens to affect code in some far off other place, it won't compile. In JavaScript you would end up with a runtime error and be wondering what is going on. With TypeScript the compiler will tell you right away what the issue is.
I found it incredibly helpful today when we had to completely refactor an Angular service method. I wanted to remove a parameter. It was called in various places, and all I had to do was run the compiler and get back "can't do it, go check XyzComponent.ts line 51" and give me a link to it. I'd click, go right to it, change the call site and repeat. After a few minutes it was compiling again and it was clean.
Sure, you can change function signatures in JavaScript and go and manually find all the places that function is called, but what if you miss one? A really good IDE can probably figure it out, much like they can sort of handle intellisense for raw JavaScript code. But with the compiler you are ensured that you got them all and everything checks out.
That's just one simple example.