To a point - I think there are plenty of people who still call it Ayers Rock and I think it is still officially dual named.
But there is a another issue - the push to use Uluru rather than Ayers Rock has been driven at national level I believe. This push for Yr Wyddfa only has come from Gwynedd county council (and even then not sure this is an official motion), so at a very local level. And there is the compounding issue of the National park - with I suspect a strong push back against renaming it Eryri (even in the English language), which isn't really a recognised name in the way Yr Wyddfa is. And the renaming of Snowdon is unlikely to gain much traction if the national park with it at its centre remains Snowdonia.
There is also the issue of the dual language policy which is in place throughout Wales - so the names Yr Wyddfa and Eryri are prominent in the Welsh language component of the dual language policy - so it seems a little odd to then request that the English changes part of its name to the Welsh.
https://www.snowdonia.gov.wales/authority/news-and-media/park-logo
I've been thinking about this overnight and I think there is a larger issue.
Wales has a dual language policy - in other words all public documents, names etc etc need to be conveyed in both Welsh and English.
Now when it comes to place names the situation is complicated by different naming conventions.
So in some cases there is only one accepted name (typically a traditional Welsh name) and therefore both the English and Welsh language will use the same name - e.g. Tal-y-Bont, Croes-Goch, Cader Idris and hundreds of other names of villages etc
In other cases there are variant spellings of the same name in Welsh and English - e.g. Wrexham/Wrecsam, Cardiff/Caerdydd
But there are others where the English and Welsh are entirely different names, not related to each other at all, Snowdon/Yr-Wyddfa being a good examples, but so to Swansea/Abertawe, Fishguard/Abergwaun, Cardigan/Aberteifi, Tenby/Dinbych-y-pysgod.
So under the dual language policy we use Swansea in the English language, but Abertawe in Welsh etc. Now if the rules for Snowdon/Snowdonia are to be changed such that even in the English language we use Yr-Wyddfa/Eryri and Snowdon/Snowdonia are lost entirely it sets a challenging precedent - one which if adopted consistently would mean that Swansea, Fishguard, Cardigan and Tenby would cease to exist as place names, even in English.
There is another point, which sets Snowdon apart from other examples used in articles on the subject, most notable Everest and Ayers Rock. Snowdon as a name does not come with colonial baggage in the manner that Everest and Ayers Rock do - they are named after colonial settlers which I can see may be increasingly unacceptable, Snowdon simply means snow hill which seems a perfectly acceptable name for the mountain, and no less acceptable than the barrow which is what Yr-Wyddfa means.