First, the all/some time relations are only defined where the relation is time-dependent in the
first order BFO theory. The realization relations are not time dependent. So the first part of an argument for there being some/all time relations would be to argue why the realization relation should in fact be time dependent.
I don't think it makes sense for the inverse, at least. The "all" or "some" time is the time the subject exists. Consider a typical role, a nurse role. Typical realization: attending to a patient. Person gets a nurse role when they are licensed, say Jan 1, 2021. There are a bunch of realizations, several every day that the person works. Pick one of them, say the one (call it b) that starts 1:15 and ends 1:30 on Feb 2, 2021, and assert that b is a realization of the nurse role.
What would it mean for the nurse role to be realized at some time or all times during the encounter? I can't see that anything would be gained by the relation being time dependent, given that we know when the process is, when the participation is, and when the person has the nurse role.
But maybe the realization relations should be time dependent. How about trying to come up with a theory of what the temporalized relation would mean, a scenario where an all times and some time realization are possible and distinguishable, and demonstrate a realizes assertion and an a putative inference such that
a) the inference is valid when the some-time assertion is true,
b) the inference would not be valid in the absence of the some-time assertion,
c) the inference would not be valid if the all-times assertion was made.
We don't have many
axioms for realizable entities currently. We say that the realizable has to exist at the start of the realization, and we say that the bearer of the realizable entity has to at some time participate in the realization. It may be that there should be other axioms - suggestions welcome.
Alan