The advantages and disadvantages of CI's cemetery status have been debated previously. To me the greatest disadvantage is that cryopreservation procedures may not be performed on-site. A local mortuary is used for that purpose, after which the patient must be transferred by vehicle. A second disadvantage is that when you've surrendered yourself to a regulatory authority, you depend on it for your continued right to exist. I can imagine a situation where a hostile official replaces a relatively friendly official, and CI could find its cemetery status in jeopardy, with the threat that it could have to turn over all its patients to "another cemetery."
By remaining unregulated, Alcor retains the right to run its operation in any way it wishes. It does not have to provide little holders for flowers for each of its cryopreserved patients, for instance (as CI has to, as a cemetery). I'm sure there are other, less frivolous issues.
Regarding the classification of procedures as "research," one reason why CI may have had no need for this is that it doesn't do any standby/stabilization procedures.