This may or may not be a useful default, that probably depends on the type of community, but I’m not sure it really solves making personal messages more accessible in searches.
In the context of private support, it seems reasonable to assume that it will be strongly related to the community at large, making it likely that there will be similar topics/posts and could produce a lot of noise around the personal messages a user might be searching for.
In the same way that categories get computed titles in the suggestions, perhaps in:personal could benefit from its own associated title to make the suggestion a bit more friendly.
For example, if I start a search while viewing the feature category here, I will see this:
Image may be NSFW.
Clik here to view.
and selecting that will add #feature to the search query. For personal messages, that could be something like “in Messages” where selecting it would still add in:personal to the search query.
