I run SPDs but occasionally swap to flats for a change.
SPDs make technical climbing a bit easier (for me anyway) and give me confidence on drops that the bike won;t fall away from me
Flats make me realise needing SPDs on drops is because of poor technique, and they tend to help improve my cornering.
The other thing flats do is position your foot (perhaps less so with newer enduro SPD shoes) further forward on the pedal. This means all of your weight is slightly further forward, which helps in the corners as there’s more weight on the front tyre. The lack of float also means it’s easier to steer the bike with your hips.
I find flats get a bit frustrating when the trails are slippy, as it’s much harder to catch a rear wheel spin and keep going.