Bluetooth always adds a bit of lag. It has some frequency hopping tech (for avoiding 2.4ghz wifi) and two-way communication syncing and stuff that causes this, IIRC. It's not a lot, but it is there. I assume modern consoles expect it. Even then, at competitive events they generally use controllers wired.
The RetroUSB NES controllers use straight up oldschool 2.4ghz RF chips instead for this reason. Bluetooth has more protocol lag, so to speak.
Then again, the error correction of BT is better when there is interference...better a button press a split second late than dropped. Trade offs.
As far as the diagonals, yeah, they are very easy to hit...causes the biggest issues on something like Contra that you need to shoot down/forward and then suddenly duck.
There's a tape mod for the older 8bitdos that is supposed to help. You can Google for some pictures on Reddit and the like. They are super easy to open up and work on. I've been fiddling on and off for a few days with a tape mod, but haven't quite gotten it where the diagonals are harder to hit for something like Contra, but not too hard for something like Street Fighter II.
Got pretty close though. Feel like I'll get there eventually.