Service revolver barrel length has traditionally been 4" or longer. Such guns were and are carried openly in a side holster. Under 4" has traditionally been a length reserved for concealed or plainsclothes carry.
The limit is not arbitrary but has been set by custom over the last century or so. It is arbitrary within those limits. Below 4" is considered less than a duty sidearm and hence for concealed carry or a snub.
If the limit is 2.5 what of 2.75? Round butt N frame with a 2.625" barrel in .45 Colt, a snub
tipoc
Exactly. One only has to look to the defacto standard service sidearm of the 50s and 60s, the S&W M&P Revolver, and it's K-Frame offspring. The M&P was offered in 2, 3, 4, 5, and 6" Bbl lengths. The 4, 5, and 6" models were considered standard service guns, while 2 and 3" pieces were generally reserved for backup, plainclothes, and concealed carry.
If we really want to complicate things we can look at the world of autoloaders for comparison. With, according to them, over 80% of the US Law Enforcement market, The Glock family of pistols have become the defacto service pistol of our era. The full size 17/22/31 have 4.49" Bbls, the midsize 19/23/32 have 4.02" Bbls, and the downright snubby 26/27/33 have 3.46" Bbls.
I think it depends heavily on the weapon. A 3" J Frame is on the long side, a 3" or shorter K Frame is pretty short, and an L or N frame thats anywhere under 3.5" looks downright short. Basically there is no rule, aplly your own judgement.