The only reason I can think of to Why Not, is that belief systems, traditions, and cultures around Spirit Animals are very different. Some traditions do not include reincarnation. Some traditions of reincarnation do not include cross-species.
Spirit Animals to me also include Therianthropy and Zoomorphism. So, for some people, a spirit that is an animal is more like a symbolic correspondence to something else. So, that can be much less individual.
Some spirit animals are considered the guardians of family lineages, so that's slightly less individual.
But if you individually feel that a past life version of yourself is also acting as a spirit animal, then why not? I didn't think that past lives could be dis-associated, but Gordon Michael-Scallion wrote on it and I technically sat in with some past life regressions that made a conversation with a past life part of the process. Different lives mean different egos. If your spirit animal wants to associate with you again, and you want to welcome that part back, then why not?