They absolutely do IMO, in 2 ways
- Whenever I need to hop into a code share w/ a co-worker (I'm remote FWIW) the ability to quickly suss out an idea has greatly improved from having a decent aptitude with those types of exercises.
- Any non-trivial PR usually has at least a few portions that could be extricated to challenges like these. Being able to slice through issues like these in 15-30 minutes vs. say hours helps w/ my cadence. It lets me focus on the issues that are unique to the business.
The 30 minute pairing challenge we give during our interview (which I took myself) was something that was pulled and simplified from our source. I ended up having to implement something very similar just weeks after I started.
Of course being good are things like this isn't necessary to being an effective sr. developer, nor is it sufficient (even for an entry-level). But I do very much see it as a skill that is helpful and worth getting good at.