As long as the phone is sufficiently thin, I don't really care about additional thinness. I'd much rather optimize the other two spatial dimensions.
The phablet trend is annoying. Most options are oversized. For me, the phone needs to fit comfortably in my left front pocket in a way such that (after getting used to it) I don't really notice it's there, and I must be able to grab it and hold it comfortably with my left hand plus use my left thumb to unlock it while holding. It needs to work in rain and snow conditions, and it should be durable enough it doesn't crack or otherwise break from minor accidents. Battery capacity should allow for 1.5-2 days regular use and should not detoriorate too much over the years. There should be 8-10 years or so of OS and security updates, and the OS should be as stock as possible without the provider loading it up with their custom stuff and added bloatware you can't remove.
When I had to replace my phone around a year ago, I ended up with a (at the time) previous generation Google Pixel model. Was a bit larger than my preference, but size still works for me after getting used to it. If size was the only criterium, I would have gotten an iPhone (which is not my thing, but for all of you who prefer it, good for you). Could have gotten a free phone from my workplace, problem was the only two options was an iPhone (as mentioned) or a Samsung phone (which around 15 years ago after experiencing the Samsung ecosystem on my at the time phone, I promised myself I would never ever buy a phone from them again). So for me, the value of form factor, function, support and no bloat, exceeds the value of getting the phone for free. But if thinness was the only difference, with the free one being slightly thicker, I would have taken the free one in a heartbeat.
Bonus of keeping your mobile phone in the front pocket rather than on tables etc wherever you are; you get to focus on the stuff around you rather than your phone, you don't keep forgetting it, and as you're not constantly putting it out on display it doesn't matter that it's not the latest most expensive model (if the people around care about that sort of thing, in which case I'd say surround yourself with different people) because it's in your pocket and most of the time not visible.