The downside is that to get the size optimization, TLS servers will get moderately more complicated (they'll need to have multiple MTC certificates configured and select the right one depending on the client's state), and TLS clients will get considerably more complicated (they'll need to continuously download landmarks for each CA out-of-band from a trusted source).

I expect many non-browser TLS clients won't support the small landmark-relative certificates, because there isn't a clear party to operate the landmark distribution service (Chrome has Google, and Firefox has Mozilla, but who does curl have?). I'm also worried that support will be lacking in open source TLS servers, though that's a more tractable problem. Consequentially, I expect the large standalone certificates to be quite common outside of connections between browsers and CDNs.