Interlining was pretty much what killed BMI financially, being Star Alliance they got all the interline connections at Heathrow to UK domestic and near European points, but by virtue of the way that through fares are divided between carriers where there is a long haul and a short haul, just didn't get adequate revenue. For carriers like BA who have both long and short haul through Heathrow, it's just an internal accounting exercise, but for BMI who didn't have the long haul it was different. BMI also got stuck with all the costs of mishandled baggage, it being the final carrier who bears this cost as they have the local presence, but if say Air Canada decided to leave some bags off in Vancouver because they had a heavy cargo load and were beyond MTOW, it was BMI who got stuck with the bag repatriation costs at Aberdeen or wherever.
Having said that, in the USA, now we are down to a minimum set of oligopolist carriers who pretend they serve every journey but in practice do not, it falls to the FAA as the regulator of what remains to be regulated to ensure that passenger convenience is not further stripped away in a search for ever greater margins. They seem to be conspicuously failing in this, constantly being out-manoeuvred by the mega carriers' many lobbyists in Washington. It seems about time for a different head who understands what a government needs to do in such a minimum carrier choice situation that they allowed.