Regarding the iterative instability issue: FHorz problems are, by nature, very finite in their iteration counts. Moreover, each such iteration is actually presenting its own legible data at each iteration step. InfHorz solutions are approximated by iterative solutions that could cycle through hundreds of iterations until they are deemed converged. And such convergence may fail (which does not directly happen in the FHorz case–it’s diagnosed in other ways, see Deadbeat agents and feasibility constraints).
Since the toolkit already tells one when InfHorz fails to converge, and since it’s really not a problem in the FHorz case, the safety is there.
I also suspect that the real gains will be found in the FHorz cases, because there are so many more interesting dimensions to the Household problem than the Firm problem. But perhaps that’s just my bias/experience talking.