Back when i was living that pixel life I let my pixel float around in my pocket in the nude. Then one day the screen got screwed up from a fall. I filled out the form, sent google my $100 to repair it, printed off the shipping label, sent it off, and never received it back, even after months of emailing back and forth about what the hell.
I could have saved all that with a $15 piece of rubber.
I have one of those ultra-thin cases that's like two sheets of paper thick and doesn't protect from anything but scratches on my pixel 7, because otherwise the back is so slippery it goes flying off whatever I set it on if someone walks across the room.
Usually something fairly minimalistic. Memumi ultra thin, little, to no extra bulk, frosted design, protects against scratches, & small drops, but that's about it..
I use the Rhinoshield carbon SolidSuit and it's worked great on my Pixel 6 since I got the phone at release.
The Dbrand grip has looked tempting, but I don't have a need to get another case as this just works and works well for me.
Case and screen protector. Always. It's already a large phone with an awkward camera bar; the case helps even it out and gives something to grip on to.
Case (Spigen Liquid Air). No screen protector (curved screen). Wife had an old pixel 3 and it shattered to a million pieces (front and back), so case it is.