The alliances are basically just loose affiliations of carriers to facilitate codesharing (buying a ticket from Air France that actually involves flying on a Delta airplane), mileage earning, mileage redemption, and lounges. Unless there is a joint venture immunized against anti-trust/collusion lawsuits (from SkyTeam, DL/AF/KL/AZ have such a joint venture for trans-Atlantic traffic, as do BA/AA/IB from OneWorld...I think there's something in Star Alliance as well, but I'm not certain), the carriers must all still compete with each other. These are massive companies with their own IT infrastructure, and integrating it is highly nontrivial. NW and KL had something great going on, but the AF/KL combination and then the NW/DL merger did a lot of damage to that (largely because of DL's choices of IT systems to preserve). Within any of the alliances, you'll find varying degrees of IT integration between their systems.

As has been pointed out, SkyTeam has several frequent flyer programs (as do all the other alliances). DL has one. OK, VN, CZ, KE, MU, SU, CI, AM have their own. AF, KL, KQ, UX, and RO use Flying Blue. In Star Alliance, you'll find Miles&More used by LH, LX, and OS. BD has its own program. NH has another. AC has another. UA has one, and its merger buddy CO still has a separate program of its own. To credit miles to a specific program, you need to give your number before flying or else provide documentation. Apparently M&M is willing to hunt things down based on electronic information submissions. Most programs aren't, and the IT systems are not integrated enough in any alliance for this to all be done automatically.