Yes, of course that plays a role as well.
But we need to keep in mind that AMD at this point is much more margin driven than Intel, as funny as that sounds. So if AMD can it will take all possible big margin markets. While a significant part of the total market by revenue, quantity wise that will still be little of the total market by units volume. While AMD will continue to reliably participate in lower margin sections to keep a foot in, they'll likely keep plenty of it up for grabs.
Intel on the other hand will want to keep quantity up to keep their fabs (respective obligations with TSMC) filled. Only once they get quantity wise significant outside customers for their fabs this may change.
I was somewhat disagreeing with part of your post, where you said that "quantity" or capacity is Intel's competitive advantage.
I think that only plays a role in tiny phase of the semi-cycle when there is a severe shortage. In all other times, TSMC can ramp up or re-allocate capacity to satisfy all customers.
Just look at NVidia, for example. NVidia was able to ramp up from almost nothing (single A100 product at TSMC) to all of the client GPU, all of the server GPUs and also the new Tulip mania for the AI cards.
Nothing would be stopping TSMC from providing all the capacity AMD needs to take over Intel's market share, since that share gain would be permanent for TSMC, while Intel can (and in fact is planning to) screw TSMC and move the production to its own fabs.
I will only believe that we have a level playing field when 2 equally competitive products, priced at the same price, split market 50:50. Intel
gaining market share in client last 3 quarters, to a grotesque degree / market share breakdown is an indication that something else, something fishy is going on...