You can solve this issue by providing a general webservice, with credentials as parameters of the webservice itself, and then use the executeMicroflowAsUser from the community commons library (after you have checked the credentials ;-)). CurrentUser will be available in that microflow.
I recommend filing a feature request to have this changed, I can't see an immediate reason why webservice users shouldn't be able to log in normally too. There used to be differences in how they were handled in terms of licensing, and in the past you weren't able to login multiple times with the same users, but this is no longer relevant as you can allow logging in multiple users now and webservice sessions are treated normally. Maybe I'm overlooking something that is preventing this from being possible to change, but you can always try.