Just how slight is the benefit to keeping them? I reckon it's a lot more than slight. In addition, selling LHR slots does not deal with the FR problem, in fact it would add to the already considerable cash pile EI have and make it even more of an attractive take over target by people/companies interested in nothing but that cash pile.
Selling the slots to BA would mean EI having no control over them, and who is to say that BA wouldn't reduce services from DUB/ORK/SNN/BHD over time especially if as you say extra slots would mean them better able to compete on other routes?
Finally, just because BA doesn't hold the same % of LHR slots as AF does at CDG does not mean they are short of slots. Don't they already lease some out to other airlines?
When I mean selling their LHR slots would fix EI biggest problem (FR), what I meant that as part of a posibble deal, BA (joinly with EI) could buy back the stake held buy FR, meaing that any FR takeover by any other airline would be imposibble (with the Irish Government and IAG holding a majoirty of the shares) in return EI sells their LHR slots to BA
With the sale of the LHR, EI can codeshare (maybe even a ATL style deal even) on BA's LHR-DUB/BHD services, which would mean more passengers use then (EI's and BA's) and BA can cut duplicate frequncies (and use then for new routes), which would mean yields will rise making them more profitable and in turn meaning its more likely BA will retain those services for the long run
What you also have to understand is that due to BA having a smaller share of slots at LHR (which can't handle as many flights as CDG) is a major limitation in what flights BA has to operate, its has to choose between:
1: Extensive TATL network
2: Extensive shorthaul connections
3: Extensive Asia/Africa/South America networks
Unlike BA, Lufthansa and Air France-KLM have all of those networks and since LHR is finding it diffcult to expand, the only way BA can better compete with its rivals by having all 3 networks is to buy more slots at LHR/LGW, including EI's slots at both airports...