If nothing else, it would show that the government is finally getting serious about getting this thing under control. Domestic rule compliance would also go up if they’re seen to be serious... and of course people shouldn’t be going for leisure travel at the moment anyway.
But more importantly, as I’ve said before, stopping people entering the country (and therefore leaving in the first place) at a time when it’s expected that domestic restrictions are likely to be reduced will lead to a huge amount of leisure/holiday spending within the UK, which would be a massive boost to the economy. Yes it means also preventing foreign tourists arriving, but realistically, who else is stupid enough to come here right now anyway? So for this reason alone, I think the government won’t be able to resist the temptation, it’s realistically a one-time-only offer they have.
BA will be fine.