I'm only able to find the following about bank angles, which specifically refers to turns while in a holding pattern:
(b) Make all turns during entry and while holding at:
(1) 3 degrees per second; or
(2) 30 degree bank angle; or
(3) 25 degree bank provided a flight director system is used.
Use whichever requires the least bank angle.
This is also in the Instrument Procedures Handbook which under *High Performance Holding on page 3-25 says that a flight director has a bank angle limit of 25 degrees.
If we use the above guidelines, then a flight director will use 3 degrees per second or 25 degrees of bank, whichever is less. My calculations give us the following bank angles and associated rate of turns1:
Standard Rate Actual Rate
TAS Bank Angle Bank Angle of turn
80 13.17 13.17 3.00
120 19.34 19.34 3.00
160 25.08 25.00 2.99
200 30.33 25.00 2.39
240 35.07 25.00 1.99
280 39.31 25.00 1.71
320 43.10 25.00 1.49
360 46.48 25.00 1.33
400 49.48 25.00 1.20
440 52.15 25.00 1.09
480 54.54 25.00 1.00
As you can see, a jet travelling at 480 Knots TAS (not uncommon at altitude) would require almost a 55 degree bank angle to make a standard rate turn, which would be an amount considered by almost anyone as excessive.
When limited to 25 degrees of bank, this would result in a rate of turn of 1 degree per second (or a 6 minute turn). Anything over 160 Knots TAS would be less than a standard rate turn, and once past 320 Knots TAS it wouldn't even be a 1/2 standard rate turn.
As far as the 1/2 Standard Rate, they often use the 1/2 BANK autopilot mode at high altitudes. This would result in a rate of turn approximately halved, so a 360 degree turn would take 12 minute at the same 480 Knots TAS. ATC expects the normal bank in the terminal environment though, so it isn't used at lower altitudes.
As others have said, transport category jets don't even have a rate of turn indicator (it isn't required by 14 CFR 25 if you have a third attitude indicator) and they simply fly bank angles. Normal hand flying is limited to 30 degrees, which would allow a standard rate turn at a slightly higher airspeed, but then starts to taper off just the same.
That being said, the Instrument Flying Handbook does include this little tidbit in the section on turn indicators on page 5-21:
The dial of these instruments is marked “2 MIN TURN.” Some
turn-and-slip indicators used in faster aircraft are marked “4 MIN
TURN.” In either instrument, a standard rate turn is being made
whenever the needle aligns with a doghouse. A standard rate turn is
3° per second. In a 2 minute instrument, if the needle is one needle
width either side of the center alignment mark, the turn is 3° per
second and the turn takes 2 minutes to execute a 360° turn. In a 4
minute instrument, the same turn takes two widths deflection of the
needle to achieve 3° per second.
So maybe at some point in the past it was more common (or maybe faster but-not-quite-as-fast-as-todays-jets) but you just don't see that anymore. (It could be where all of the references to 1/2 standard rate turns come from though.)
1 Math adapted from the formulas here.