My Fenix 6 does not track my current pace correctly. Splits are correct but current pace often 1-2min off and never accurate.

I've noticed the same, especially on tree covered trails. On the open the pace is reasonably accurate, but once I get even slight tree coverage, the pace on the watch always slows down compared to my actual pace - the difference is typically 0:30-1:30/mile which is consistent with your observation. 

I have actually written a script to automatically analyze a run and compare the "average instant pace" to the mile splits, and I see a consistent bias towards slower than actual pace.

See my post here: https://forums.garmin.com/outdoor-recreation/outdoor-recreation/f/fenix-6-series/226504/instant-pace-bias-towards-slower-pace

Not true. I've used Suunto watches before that implement FusedSpeed algorithm. I'd say that in Ambit3 Peak the instant pace was usually spot on. In Suunto 9 instant pace was a bit more optimistic but still way more accurate than completely useless instant pace on Fenix.

I am pretty sure Fenix does try to fuse GPS based pace with data from the accelerometer, because when I stop the pace reacts very quickly and stays at zero until I start moving. But whatever algorithm Fenix implements, it is certainly faulty.

This seems to be the case, unfortunately.

For me, instant pace typically varies in the range of 2 min/km. This is as bad as your observation...completely useless, and frustrating.

For many, it seems to be an acceptable solution to invest $220 more to get a Styrd.

I find it problematic that Garmin pushes features, such as PacePro, that would require relatively accurate pace information while not delivering the required performance. Obviously, a device that is within Garmin GPS specification will not be able to track pace accurately: Garmin® GPS receivers are accurate to within 15 meters (49 feet) 95% of the time. Generally, users will see accuracy within 5 to 10 meters (16 to 33 feet) under normal conditions. 

Tend to agree with Former Member, there is likely something wrong in the Fenix implementation, not all products hurt this bad - SportsTracker app on my Android phone delivers far more accurate pace information than my Fenix 6.

GPS specification will not be able to track pace accurately: Garmin GPS receivers are accurate to within 15 meters (49 feet) 95% of the time. Generally, users will see accuracy within 5 to 10 meters (16 to 33 feet) under normal conditions. 

This is for car devices

For watches it's:

"The GPS location accuracy of Garmin outdoor watches is around 3 meters (10 feet), 95% of the time. "

support.garmin.com/.../

Besides having a Stryd-like foot-pod, you're out of luck for the most part. Usually you'll notice that the first few seconds of a jog/run/walk aren't even registered in the pace data-field. Honestly, the best thing Garmin could do IMO in this regards is to add a rolling average pace similar to they do on cycling power: 3second, 10second, 30second average pace, etc.Would have less noise and a lot more meaningful to maintain a pace than lap-pace.