I don't think you understand what cat heat is.
Cat heat is exactly the high RPM start with SAI.

If you turn it off, it does not do it anymore, it only keeps the idle as high as it needs to be.
The engine does not start "like it was already warmed".
In 99% of cars there is zero issues turning it off.

So, what problem exactly are you having?
There is still idle speed based on temperature and also torque reserve is different, and this is more noticeable in sub zero weather.

If you have issues with the idle after start, then most likely you have mechanical problems with the car.
Number one reason is vacuum/boost leak, then bad injectors, bad plugs or bad compression.

If you have checked all of those and you are sure, then I have seen once or twice (out of THOUSANDS of cars) where the non-catheat cold start is not calibrated well.
This was on a couple S18 software versions. Never ever seen it on Bosch.

I'd start with an intake pressure test though.

I've turned off cat heat on these many times, zero issues.
Car has mechanical issue.

Carbon in inlet makes zero difference at idle.

Cat Heating is only on cold starts or half cold starts. You may be talking about cat purge if your talking about milage... which idk if it applies to this application CLRSHK.

IDK about MED17 but when you turn off FHOKH the routine typically doesnt run ever... which causes emissions systems to never finish their tests and cause some to say incomplete forever.