F1 merging with LMP is just F1. If that happened then another LMP type class would have to emerge because the point of the class is race at Le Mans.
Formula E exits because it's a technology that can now be used to go racing, but F1 has not chosen to go down that road (yet). If F1 wanted to include electric technology, then FE is at the effect in how F1 uses it. If F1 wanted to use electric cars along with hybrids, FE will exist as designated electric class. If F1 wanted to go all electric, then FE as it is will stop (whether it the relevant stakeholders like it or not).
Formula E exits because it's a technology that can now be used to go racing, but F1 has not chosen to go down that road (yet). If F1 wanted to include electric technology, then FE is at the effect in how F1 uses it. If F1 wanted to use electric cars along with hybrids, FE will exist as designated electric class. If F1 wanted to go all electric, then FE as it is will stop (whether it the relevant stakeholders like it or not).