In a top notch system, most, if not all the electrolytics caps are not directly in the signal path. Speaker crossover capacitors are, and get the full brunt of amplification. What is actually audible is a variable that’s difficult to quantify, but it’s better if they were good audio grade poly caps instead of the electrolytics, and it’s a fairly simple thing to upgrade....at the very least, bypass them with a small value poly cap.
It’s a similar logic to better wire, better connectors, etc. At some point, just about everything makes some difference.
Regarding the importance of sensitivity...I suppose it depends on how loud you want to listen, and the size of the room. I’m using primarily about 17 watts triode tube power into 89db speakers in a fairly good size carpeted room. I have the option of exceeding 30 watts in Ultralinear mode, but rarely ever the feel the need for more power....it seems to get plenty loud enough to annoy the family. There is an active subwoofer in the system to help fill out the bottom octave,so I’m sure that makes some difference, but overall sensitivity has been a non-issue for me....like anything else, I guess it depends....the transparency gained by better caps and wire means far more to me than a little extra volume level.