I picked up my radar-less M3P (no FSD) yesterday and already have 100 miles on it. Prior to this, I spent 18 months in a company-owned Model 3 LR RWD (2017) w/FSD and the updated FSD HW, so I have a lot of experience with AP for comparison.
The weather has been sunny at times and cloudy, but no rain since I picked the car up, so I can't comment on how bad the performance is in those compromised conditions. I will say this though, I typically don't trust AP in heavy rains anyway, so I'm not as concerned about this as others seem to be. I'm sure if I lived in Seattle or something, it would be a big deal to me. I haven't driven in the complete dark yet either, but the headlights did seem to come on earlier at dusk than I remember with the old car. I actually like that change, but agree that requiring auto-high beams will suck.
So far, the AP has worked exactly the same as my radar-equipped experience, including the same flaws. It seems to track the center of the lane exactly as well as before. When a merge/right turn lane opens up, the car wants to re-center itself across the 1 1/2 lane width (so it shifts to the right for a bit, annoyingly). As expected, I don't see two-cars-ahead anymore since the camera doesn't seem capable of doing that radar magic. Stop and go behind other cars feels just as smooth as before. The increased following distance (basically you can't set it to less than '3') doesn't matter to me in country driving because that a fairly rude following distance anyway. But in heavy traffic or on highways, I typically run at '1', so I'm hoping this issue is fixed very soon. Also, the 75mph speed limit sucks, but I couldn't care less about "emergency lane departure".
There is one very tricky corner nearby.. a very tight, decreasing radius turn on a country road that takes a typical driver down from 50 mph all the way to about 10mph. AP has about a 50/50 success rate around this corner. I've only tried it once with the new system and it failed - I had to take control to avoid overshooting the corner, even though the car had slowed WAY down. I can't imagine how radar could help on a corner like this though so I really doubt it's a factor. I'll try to hit it a few more times though and see if it gets better.
Last summer, with the old car, I suddenly started getting a lot of phantom braking events. I went from one event every 2 months to one per week. My wife refused to even ride in the car if I engaged AP because it was getting so bad. It seemed to happen mostly on very sunny days with very sharp tree shadows. It got better over the next year and was mostly fixed, but still about 1/month. I haven't experienced any phantom braking on the new car, but it's only been 100 miles so far, so too soon to tell.
Last night, Tesla pushed me the software update to enable the cabin camera. I'm curious how finicky this will be. Is it just looking for a warm body in the seat? Or will it freak out if I close my eyes or turn my head? I realize the camera is quite capable of all this, but not sure if Tesla has started using it to nanny up the AP. I sure hope not.
Anyway, I just wanted to share one person's perspective on the radar-less situation.