I do care about observation accuracy. I make observations of the same stuff year to year, and want the locations to match. I also make observations that lack important information, and I have to go back to the spot with someone that knows plants. I include landmarks in the background, like a distinctive tree, to be able to see where I was.
Lately the first photo takes some time to increase location accuracy. It will take 20 seconds or so to go from 3200 m accuracy down to below 10 meters, where it stops. On a good day, I can get 5m.
I second the use of GPS logger https://gpslogger.app/. It is very useful for logging and recording tracks and you can customize a lot of things. You can use the logging interval you want (as low as 1s!) and you can even have it running in the background without recording the actual locations in a file. It is a bit trickier to install as it has to be installed from a .apk file. Not sure it is available for iPhone though.
On Android I use an app called GPS Status, currently at version 11.3.315, which can also be set to keep running in the background. But I’m sure the GPS Logger suggestion is fine too. And yes, I always iNat in Airplane Mode with the iNat AutoSync setting turned off (permanently). Avoids any location confusion from cell signals, and greatly reduces battery drain. When I’m ready to upload, I turn cell/wifi back on, edit the observations to add my initial IDs, then manually sync.
Of course not everyone will want to have cell service off while iNatting - there are tradeoffs either way.