Subjectively speaking, I am very much against random D1 lynch. Objectively, I think that it's possible to argue for it though.
First, to define the term -- a random lynch is one that is not based on anything else. No specific info, no tells, no reads, no theory based on the known game setup. Purely random, with the exception of completely obvious things to account for like "don't lynch the IC".
If I had to argue for random D1 lynch in a debate, I would try to argue that the alternative is worse (obviously).
At the start of the game, there is precious little information. Barring obvious scum slips, any scummy behaviour could just as easily be day 1 jitters or even a simple difference in play style. I prefer to sit back and watch whereas others may be more aggressive. Either action could be spun as scummy -- laying low is trying to avoid attention! Aggression is just trying to push for a quick mislynch!
Trying to make sense of player actions before the first lynch and night phase is a wild goose chase. Worse, the scum have far more information than the townies at this point of the game, which in turn can give them a lot of control. Scum partner under fire? Nudge the focus towards somebody else. Townies getting angry at each other for no reason? Grab some popcorn. But scum can't defend against a random lynch.
But doesn't that mean we won't have any useful information from D1? Not necessarily. You can still do the usual D1 discussion, finger-pointing, nit-picking and wagoning. Even if these things don't ultimately lead to a lynch, they still have meaning. Sending somebody to L-1 is still pretty big, especially with certain hammer-happy players. And then you'll also have night actions to consider, which can account for a lot depending on the setup.
My actual opinion is that you can always do better than random. You might be able to glean some info out of a random lynch, but you get much, much more when you let players find reason from the madness.
I think the records show that d1 lynches in f.ds actually have a higher success rate than pure random (in an actual debate, I would go check). But even if that isn't true, there is just so much more weight to every action when the final result isn't random. Knowing that a dice roll will determine the lynchee actively disengages players who no longer feel the need to criticize every little thing that others write.
Scum can try to manipulate the d1 lynch result by turning attention and breeding conflict, but these actions can be uncovered and dissected in subsequent days.