If you look at the photo below the left turn lane was signed 'except buses' in 2019. On leaving the bus lane under the old configuration, a bus would only be delayed if there were an exceptionally large number of vehicles turning left and that still could happen (although is less likely) with the bus gate. The actual gain to buses looks very marginal to me but, there must be data on this which tells the full story.
It maybe that the bus gate actually has little to do with the perma-queue that has developed over the last few years going eastbound on this section of the High Road. When Fishers Lane closed initially traffic was regularly tailing back as far as the eastern end of South Parade from the Acton Lane junction. It looks like the phase was extended here to allow this to clear but this has reduced the flow on the High Road. This might be by design with the traffic planners preferring to the queue to form on the wider section of the road west of Acton Lane rather than the pinchpoints in the centre of Chiswick. This allows continued progress for emergency service vehicles and, for an example a driver who needs to make their way from Windsor to Pall Mall.
If this is correct, taking out the bus lane won't actually solve the rat-running problem. You are right that people 'should' stick to the A315 and the A4 but the reality is that SatNavs and local knowledge means that they can avoid sitting in a queue for a few minutes and they will take that opportunity. We can all disapprove of this but I don't see a robust way of tackling the problem that doesn't just create a different and possibly worse issue elsewhere.