As a practical matter, revocation on the Web is handled mostly by centrally distributed revocation lists (CRLsets, CRLite, etc. [0]), so all you really need is:
(1) A PQ-secure way of getting the CRLs to the browser vendors. (2) a PQ-secure update channel.
Neither of these require broad scale deployment.
However, the more serious problem is that if you have a setting where most servers do not have PQ certificates, then disabling the non-PQ certificates means that lots of servers can't do secure connections at all. This obviously causes a lot of breakage and, depending on the actual vulnerability of the non-PQ algorithms, might not be good for security either, especially if people fall back to insecure HTTP.
See: https://educatedguesswork.org/posts/pq-emergency/ and https://www.chromium.org/Home/chromium-security/post-quantum...
[0] The situation is worse for Apple.
Indeed, in an open system like the WebPKI it's fine in theory to only make the central authority PQ, but then you have the ecosystem adoption issue. In a closed system, you don't have the adoption issue, but the benefit to making only the central authority PQ is likely to be a lot smaller, because it might actually be the only authority. In both cases, you need to start moving now and gain little from trying to time the switchover.