Whatever the benefits of an alliance, an airline's lounges are primarily there to serve that airline's passengers.

If you have one airline with a small operation at a station which is a major hub for another airline in the same alliance, you'd often expect to see the small airline use the home airline's lounges. Examples: QF at LHR, BA at SYD.

If the small airline actually thinks it's worth having its own lounge at that station, the small airline's lounge is often of a poorer standard than the home airline's. Example: BA and QF at HKG. The result is that if there is any migration pressure, it's away from the small airline's lounge and towards the home airline's lounge, which is almost by definition bigger and more able to cope with "visitors".

At MIA, BA is the small airline; two movements each way each day. The size of the lounge is commensurate with the size of the operation. AA is, in contrast, an overwhelming presence.

If AA were an airline operating to normal standards, you'd expect BA to be able happily to place its pax in the AA lounge, or migration pressure away from a relatively small and poky BA lounge towards a big, better-equipped and higher-standard AA lounge.

However, the general perception is that the AA lounges at MIA are rubbish compared to the BA lounge (although that may have improved recently). Consequently, the migration pressure is likely to be in the other direction. If the BA lounge gained a reputation of being open to all AA Emeralds and Sapphires, the BA lounge could rapidly be overwhelmed with AA "visitors".

This, it seems to me, is exactly the reason why there is a capacity exception in the oneworld rules, and why BA has a justifiable reason for invoking it at MIA. BA's lounge is not primarily there to serve the hordes of AA Emeralds and Sapphires who are not flying BA; it's primarily there to serve those who are flying on BA services.