The main benefit for bmi appears to be access to BMed's markets under the restrictive arrangements in place between the UK and countries like Azerbaijan, Kazakhstan etc. For example, UK carriers can only offer seven flights per week to Baku, three to Almaty etc - and BMed holds the full quota of rights available, which means that no other UK airline can enter the routes and compete with them.
BA would have almost certainly faced an OFT / Takeover Panel enquiry if it had bought BMed itself. In this way, it has obtained what it really wants - more LHR slots - without needing to go through any of the hassle of regulatory clearances for the deal.
BMed slots do indeed belong to bmi at the moment, but there is nothing to stop them selling them onwards at any time to suit. Doing so has no bearing on the routes and aircraft - for example, you could quite happily use former BMed route rights, aircraft and crews to operate a daily service to Tehran using a bmi runway slot previously used for LHR-Paris or something like that.