It's not as simple as who allows consolidation and who doesn't. You have to know under what circumstances each one allows it and doesn't.

At Citi, they allow it upon card application. Otherwise, they're likely to claim that they only allow it once every 6 months. (But they'll do more often on card applications, if you're doing card applications more often.)

And CSRs don't always give correct answers. So just because you have one instance of Cap1 telling you once that they don't do it all doesn't prove that there's no circumstance where they do it. (I'm just not sure how many people have multiple Cap1 cards at one time and are opening and closing other Cap1 cards as well and have thus been able to try in all different possible circumstances -- ie, at card opening, at card closing, and in between.)

People tend to know much more about the polciies of banks that have cards with a lot of partners. Barclays has 3 hotels as well as several airlines, in additon to its own points program. Chase has 3 hotels as well as several airlines, in addition to its own points program. But Cap1 (in the US, anyway) has no hotels, no airlines, and just its own (mulitple) points programs.