Perhaps this suggests that memory accesses from pagewalks are cached in the L1 cache (i.e., pagewalks compete for L1 cache space)?
Is there actually doubt about this? I'd been taking for granted that page walks went through the standard cache hierarchy on recent Intel, but I guess I don't have a definitive source for this belief.
This one motivates virtual memory:
https://www.youtube.com/watch?v=3kRBVdnLBW4
This one gives a high level view of how everything works:
https://www.youtube.com/watch?v=l7HoguhFVQ4