BA route their TA traffic through Heathrow, that's their model. If the airline wanted to open a new TA base then Gatwick, Manchester and Birmingham all have greater catchment areas than Dublin (and that's even if you included most of the island of Ireland as DUB's catchment).
Yes, Heathrow runway capacity is pretty full at present, so how does an airline grab more of that capacity? ... by exactly doing what BA did to BMI, buy a competitor with some and then remove then, you get the triple whammy of removing a competitor, grabbing their asset and potentially taking much of their custom in the process.
TBH, I can't see any upside for EI in being rolled into the IAG fold. EI isn't the worlds biggest or most profitable airline, but they're doing OK and the prospects look good. Ryanair are probably happy to sell, the Irish Government under some pressure to do so, but with the official data saying the economy is doing OK, the State isn't in any rush. Etihad,the 3rd largest holder with about 4% might not be in a huge rush to enter the race given the drop in oil revenues, but a second bidder may well bide their time to see at what price the board recommends acceptace.
Eitherway, IMHO, FR won't be too upset to offload their holding at a good price, especially if a new owner is happy see underinvestment in EI's profitable routes.
JAS