I have used CarPlay from early days, over the past 6~7 years I used it over 3~4 iPhone models and over several after-market stereos as well as various rentals cars and now with LC. I did not find major issues and it has a very stable product for us. I found for all the "issues" people complaint online, it is mostly on automakers' part not Apple. Working with Apple for tight integration must not to be an easy thing since Apple is Apple.
Having that said, CarPlay on LC did seem to be a bit "stupid" that I constantly have to go into the "Device" menu and manually toggle the CarPlay switch back on. I would guess it is the car connection sequence to your Toyota app gets in the way. Why every single time I turn on the engine my phone would required me to go to Toyota app to "accept" the connection is beyond me, that seems to be completely redundant and annoying and no other car maker is implementing their app this way. This seems to be a silly integration issue. But for me it doesn't affect my CarPlay experience. It is a useful feature and I even hope they can make some apps (like real time ECU status dashboard type of things) to be used inside CarPlay. (Toyota likely won't but that is a different topic)
Another thing I've learned from Toyota is that it is a very very conservative company. Anything we consider a "fix" is a new feature in Toyota's eyes. So I actually don't expect much change, if at all, to be provided via OTA update. I am curious though what is going to happen if I keep my LC for 15~20+ years and this IVI system becomes so out of date? Would we need to install the third monitor from aftermarket part to keep our IVI modern again?