This has actually been done a few times to my knowledge. The best example I can think of is the CZW/ROH Cage of Death match. Both sets of fans were basically equally-represented and of course very passionate for their team, which gives the match even in its lesser moments a lot of energy. As well, babyface-babyface matches (effectively a neutral kind of booking) are historically very common but have fallen out of favor over the last thirty years, especially on American television. Many classic British matches, for instance, are between babyfaces.
I think that the babyface-heel dynamic is a more-or-less inevitable part of the wrestling experience, albeit on the part of the viewer and not the booker. Fundamentally, the face/heel paradigm is an abstraction of sympathy. The babyface is designed to be sympathetic because they are courageous or rule-followers or attractive, while the heel is cunning and underhanded or otherwise distasteful in behavior. A wrestler with a consummate babyface character, however, cannot always guarantee audience sympathies; they may be too boring, trite, whatever, and of course vice-versa for a heel. The viewer will inevitably extend their sympathies to one wrestler over the other, making them a de facto babyface, if only to that viewer in that moment. However, these roles can be fluid or liminal and shift throughout a match.
The convenience of the conventional, moral face-heel dichotomy is that it provides simple but largely-effective tension to engage the viewer. In other paradigms, other forms of tension need to be mined. There are of course endless possibilities, but I think that most wrestling booking is risk-averse, in a narrative sense, and so they prefer to go along the well-trodden, if effective path.
