Good question. I'm concerned with how this might impact the computation of type operations, but I guess (not sure) that there is hope if we keep to a regex language with decidable inclusion/comparison operations like we use in our refinement types.
Do you have a proposal for a syntax? Preferably one that would allow us to implement the easy ? first (as in my opening post) and then implement improvements (like your regexes) in a later version?

Something like ?(REGEX):T?

we could use the same syntax of refinement types:

regex(".*@.*\\..*"): T

Nice proposal :)

Regarding the regexp types, just out of curiosity, @klag, do you have some examples (like, that you met in production) where you needed regular expressions for types?
I guess it could be useful to check structures like

{
 "title": "My Movie"
 "metadata": {
    "movie-date" : "..."
    "movie-release" : "..."
    "movie-rating" : "..."
  }
}

where, e.g., you want to allow only for an open-ended set of leaves with the "movie-" prefix under the node "metadata".
Is that the case? Are there more complex examples?