From my observation, the main abusers of the Comiston Road cycle lanes/parking restrictions have been tradespeople working at the various private houses along that road (I count roughly 40+ along Buckstone Terrace, from the Fairmilehead lights to the Braid Road junction - not what you'd call high density I agree, but it seemed to be sufficient to require quite enough tradespeoples' vehicles to be illegally parked as to make the cycle lane annoyingly inconvenient and unpleasant to use). This despite, as you say, many/most of said properties having private drives - an issue which has been discussed not so long ago elsewhere on this forum (might even have been earlier on this very thread).
And let's not forget that before first lockdown the south end of Buckstone Terrace was a de facto unofficial park and ride served by the number 11 bus. Take away the parking restrictions and the northbound cycle lane from the Fairmilehead lights to Caiystane Crescent and likely beyond will no doubt be thick with parked cars once more.
Based on the above, if they remove the parking/waiting restrictions along Comiston Road then I reckon the cycle lanes will quickly become next to useless and might as well be taken out - which could very well by why this idea is being mooted. But hey, drivists absolutely have to be able to abandon their vehicles as close as possible to their intended destination, don't they? Er...
None of this would even be being suggested if parking in mandatory cycle lanes was actually illegal, as all logic says it should be (IIRC the history of how that managed not to be the case is also discussed elsewhere on CCE). As it is we're left with the same nonsense logic that means it's not [yet] illegal to park on the footway, despite the fact that to park on the footway one has pretty much has to drive on the footway, which definitely is illegal, and by all rational argument the simple presence of a vehicle parked on the footway would seem to be prima facie evidence of the offence of driving on the footway having been committed.