But wouldn't determining promotion/relegation/European qualification based on assumptions be a legal disaster too?
Oh yeah definitely. But it's a damned if you do, damned if you don't situation really.
The TV deals the Prem has with Sky and BT Sport etc. will contain time-sensitive clauses relating to how many games are to be broadcast per-season within a time-specific period. If the games are not put on, the Prem will default on its obligations, and Sky and BT will not pay up millions and millions of pounds. The knock on effect for this would be massive, I should imagine. Similarly, the clubs will have similar time-sensitive deals with kit suppliers and sponsors and advertisers etc., many of whom will be looking for a way out of paying up what they owe, because they themselves are probably up **** creek as well. The Prem, and all the clubs in it, have a massive interest in getting the season over ASAP, and that's before we even think about promotion/relegation/continental qualification etc.
Then as you say, determining promotion/relegation without actually playing the remaining games would lead to an almighty legal shitshow as well.
For all of these reasons, the pressure to get the season done, and to get it done soon, and to get the next season off to a vaguely normal start is absolutely huge. But for the reasons set out above I just really cannot see it happening. Best hope the Prem etc. has is to really lobby the government hard to declare football some sort of essential service and allow an exception to whatever lockdown/social distancing measures remain in place, and get the games done behind closed doors. Not sure how likely this is though, as the government will not want to look like it is cowing to these sorts of pressures, and like LT pointed out above, there are huge concerns RE: policing and so on.
Basically, it's going to get ugly imo.