I have seen (and used) different Router, Hand Power Planner, Jointer and related methods with and without jigs for certain "truing" operations, so your idea is more than plausible should you wish to go down that path.
I think back in the archives here on the TFG Forum among the posts are some different examples covering all manner of jigs like this; including one for logs and making flat spots on it. There are tons on the web as well...
Many in the contemporary world of timber framing do take the time to totally square up a timber (aka Mill Rule)...but many of us do not.
Traditionally (in many timber framing cultures) this isn't something that is taken time to deal with. The timber is planned to smooth aesthetically. "Near square" (or whatever shape is desired) is the only real goal.
Joinery is "trued" to the given geometry of the specified intersection dependent on the layout method being employed (e.g. scribe rule, line rule, edge rule...etc)
Mill Rule is a much more contemporary modality of layout, and seems to be what you are wanting to employ if going for the entire timber being squared up?
Achievable (to a point) but a lot more effort for sure...rather than the other more traditional methods.