I lost my Pixel 3 recently and upgraded to a Pixel 4 (but had a Pixel 1 as well). You skipped right to the worst incarnation - no fingerprint unlock, mediocre battery life.
Why?
Face Unlock is a godsend, Pixel 3 was my first phone with fingerprint scanner and I hated every minute of using it.
It was unreliable piece of &^*&^%&^, I had to teach it my fingers every week during the cold season (which in my country is close to 7-8 months) and during summer I had to do it only once a month maybe - during winter the air gets colder fingers dry out especially if you have allergy (and I do).
And it was slow, I did unlock with pattern faster.
As for battery, I don't feel that it is poor in Pixel 4 (I ditched Pixel 3 as soon as the preorders for Pixel 4 started), but I use wireless charging all the time, I have it at work and at home, so my phone is almost always at 100%.
And now I'm puzzled, why did they bring back fingerprint scanner in Pixel 5? Apple didn't bring it back after they jumped the face unlock wagon.
Not to mention inferior CPU/CPU in Pixel 5, it looks also worse than even in Pixel 3, but the price is still premium.
So basically now we get a Nexus quality phone with Pixel price point.
I'm having the exact opposite issue -- going from the Pixel 3 to 4, Face Unlock is absolute trash. With FP I already had my finger on the reader as I was pulling my phone out of my pocket / picking it up, and it'd be unlocked and ready by the time I had it held up. Face Unlock fails every other try, adding a few seconds to the unlock, it doesn't work with masks. It's super frustrating and no amount of re-learning is fixing it. Pattern/PIN unlock isn't an option (keep in mind this is also your encryption key for full device encryption), so having to type in a passphrase even occasionally is a PITA.
Otherwise I agree, my battery life feels fine, and the upgrade to the 5 doesn't seem all that worth it.
Oh, in my case Face Unlock is reliable, sometimes to reliable, when I try to put my phone away it suddenly unlocks because my face was near :)
Oh and a trivia about Pixel 4 Soli (which is a gimmick, nothing more), I was wondering why my music suddently restarted so frequently when I was in car.
And I found out why after few days - since a week we have a lot of rain, so when I drive I have windscreenwwipers and this was somehow being picked up by soli (when my phone was mounted near windshield, but not that near) :)
Yeah I had to disable the proximity sensor for the music controls, it 1) triggered constantly when I didn't want it to, and 2) took 4-5 tries when I actually tried to use it (ie swipe to the next song with dirty hands in the kitchen). It's a neat idea, just unpolished.
I'm surprised you had as much trouble with the Finger scanner as you did. I never had to retrain my fingers in all the time I've owned it (going on 4 years now)
I live in the Canadian prairies, so cold + long winters are no stranger to me, and the fingerprint just always worked. The face unlock fails more in the winter because I'll be wearing a scarf or headcover which renders it useless. Heck, even in the summer it fails frequently because I'll have sunglasses on