Happens with all the Standard cars when using Fully Custom Transmission and I heard that a few Premiums suffer from this too
Problem is also present on some cars that are manual clutch/trans in real life...
...like Sauber LMP, and Ford GT GT40 '69.
It will also not work on the Rocket car, the clutch for the real car is only used to engage into gear from neutral. Once rolling its driven like a clutch-less sequential.
The new BMW M4 coupe will only register the gates, and auto-blip the revs, clutch does not work.
Reason: real car is spec'ed with either a DCT or auto-blip box.
I believe the same is true (DCT) for the camouflage-clad test C7 prototype vette.
On the flip side there are a couple of cars that allow you to use clutch although the real-life version is auto or DCT providing the car's stock GT6 transmission (non-custom) is used. One of those is the Jaguar XKR-S '11.
I cannot recall what the other was, if I do I will come back here and edit the post to add.