>"Wasn't this single feature half the reason you use TiVo in the first place?"
No. That was a feature added many years after the start of TiVo. It is not necessary, nor does it even work on half the recorded content. The skip feature is a single press to jump through the commercial section, you always have the option to just zoom through the commercials manually. I have not watched commercials for at least 35 years- first by recording painfully with VCR, then conveniently with several models of TiVo (my last/current being the Roamio).
>"The other half is just being able to record the show and watch it whenever you want."
That is one of many features (of course it is the base function of any DVR). The killer feature of TiVo is its ability to learn what you like from your recording and ratings and then
1) Accurately track and record every episode of everything you want with zero intervention. It will shift the schedule or even channel if necessary, across year after year. And do it intelligently so you don't end up with 10 of the same episode.
2) Predict other shows you might like and fill the rest of your storage with many hundreds of hours of things you might want to watch, so there is always something to watch and discover. Yet those recordings never rob space from anything you indicated are important.
And I have yet to see any cable company's DVRs do those. Probably due to patents. Doesn't matter anyway, time is ticking and the whole concept of cable TV is dissolving and I will be left with nothing but "streaming", which is still currently inferior in several ways, and not likely to improve. (And streaming on a TiVo is a mess of slow and annoying. For streaming, I use a Roku Ultra).