> Being a "front" suggests an entire business model created by and built around propping up that third party such that the two are indistinguishable actors on everything but the surface level.
No. One party being a front for another party suggests that the two are indistinguishable actors on everything but the surface level, or more accurately that any action taken by the first party might be better viewed as being "really" taken by the second party, that any information given to the first party is also being given to the second party, etc. It does not suggest that fronting for the second party is the only thing the first party does, or that the first party was created to serve the purposes of the second party.
Taking an example out of the dictionary, it would be unusual to claim that a massage parlor serving as a front for prostitution is obviously, by its nature as a "front", unwilling to provide massages.