That would eliminate Greenford itself, unless reopening the low level station there. There is no need to go into central London however, just change at Greenford and one of the Ruislips to access the Chiltern services.
Unless you’re one of a handful of people willing to put up with several changes and using only the stopping services calling at West Ealing, then also one of the stopping Chiltern services calling at the Ruislips, it would likely be far quicker and possibly physically easier (depending on requirements) to go via London and the Bakerloo Line.
There are a few people, predominantly local or those at the mercy of random journey planning software outputs, who’d go via Greenford, but they really would be few and far between.
In other words, West Ealing and Greenford / Ruislip aren’t especially useful interchanges and you have to factor in the lack of desirable “fast” services calling at either. It’s a shame really, but I’m not sure what could be done without proving there is huge demand between the GWML and the Chiltern Mainline and improving infrastructure / timetables on the back of that.
I just can’t see it happening.
(And I reckon most Londoners wouldn’t know all that much about the West Ealing - Greenford service, nor would especially care much if it was extended - and as for someone from outside the area doing a journey such as Reading to Leamington or Slough to High Wycombe, they would likely already have alternative options which would be hard to replace in this way.
A better option would be to consider routing traffic to/from the Chilterns via the new interchange ideas at Old Oak, with journey opportunities from a number of directions including places further south, such as Heathrow and beyond. And this is obviously what is already being looked at, to some degree.)