2.0mm at the 12th fret is pretty normal for an electric, and is what most PRS guitars are set to at the factory. String height at the 1st fret should be much lower. Perhaps have your guitar tech adjust the nut slots to get the action lower?
I run my electrics at ~1.5mm at the 12th fret. That’s about as low as I can go without getting fret-buzz on my guitars.
Measurement is normally from the top of the fret to the bottom of the string, and is done with no capo.
Certainly feels wrong, I did use to do modules 1 to 8 and the F was very hard, much easier on the new Telecaster. I wanted to try and sort myself for confidence and old cheap guitar, which I would keep as a backup if I can make it more playable. Ordered nut files and a string action gauge …
Was thinking I would have to remove the nut and sand down the base of it as saw somewhere that the string slots should be 2/3 the string diameter in terms of depth…?
Removing the nut and sanding it down will reduce the height of all the strings by the same amount. With the nut files you can lower each slot independently. The bass strings need more space to vibrate without buzzing than the treble strings.
By the way, I measured the distance from the top of the first fret to the bottom of the low e string in my guitars and it’s about 0.5mm.
Before doing anything to the guitar, especially the nut or saddle. Make sure you are measuring action and relief properly.
To measure action at the nut, fret the string at the second or third fret and measure the space between the bottom of the string and the top of the first fret. It should be almost nothing, but still something. Barely touching or barely not touching of that helps.
To measure relief, tune the guitar and fret at the first and twelfth fret. Measure under the low E at the 6th fret. Usually something like a business card thickness is adequate. If not correct adjust the truss rod.
After the above two steps, measure action, un-fretted, at the 12th fret. Bottom of string to top of fret. This is a bit personal preference and is different for each string. 1.5mm to 2.25mm may be a range for an electric. But look it up, I don’t play electric. Adjust this at the saddle and only at the saddle.
I got it with the head broken off the neck about 1980 or so, it was OK after my father and I fixed it up. Metal plate and fibreglass I used for a year or so. I had the nut done around 1998 after not playing for some time but did not manage to restart the guitar journey due to the arrival of children. I started again around September 2021, it wad hard to play. I bought a Squier Classic Vibe 50’s Telecaster and found that so much easier to play. That went back for a repair under guarantee last week, so I dug this out and restrung it to use in the interim… I managed some F chords tonight… Wait till I get the Squier back…
Yes that is high for the first fret. Nut would need to be filed. Then guitar reintonated.
Another effect of a high nut is that notes in the first couple of frets may be sharp from the increased distance.
Personally I am happy changing anything with screws and bolts, filing a nut I would get a luthier to do. Maybe when you get your Tele back, think about getting a full luthier setup on the LP to see how good it can play.
Reading about filing the nut and maybe if a slope on front of nut changing string overall length fractionally, then the tuning and intonation issues, maybe a job for a professional. It does have some sentimental value as my father and I rescued it from he scrap heap.