1. We don't know if there is a mechanic that would make not lynching someone on the first night a bad choice. But the counter argument to that is we don't know if there IS a mechanic that would make lynching someone on the first night a bad choice.
This is very fair on both sides, and why I am more open to no lynching when the setup is known and it makes sense.
2. If we don't lynch anyone, it makes the conversation dead. But the counter argument to that is: What useable information do you get out of randomly picking someone to lynch?
It can't be completely random because the mafia know who is mafia and who isn't, so despite their best efforts to mask it, they have to have some reason for being willing to lynch someone, especially if they're townie. Everyone else ideally has some sort of reason that you can push them on, even if it's something dumb like being completely random.
3. Not lynching someone would extend the overall game length, which is a concern with inactivity. But the counter argument to that is: If someone goes inactive, then they will be lynched.
Inactive people completely kill games at the end because town can't risk lynching someone just because they're inactive anymore, but they also obviously aren't contributing to finding scum. Once it gets far enough it's basically a guaranteed scum win because there will be more active mafia than there are active townies, so they can just pick apart one active player and there's basically nothing town can do about it.
Are there anymore arguments for or against lynching someone on night one?
Since you asked ...
Rule of thumb is that 1/4 of players are scum.
So that's 3 or 4 scum in this game, meaning 10 or 11 townies.
Even at deadline it would take 4 townies to lynch a scum and resist influence from the scum to lynch somebody else.
A day 1 lynch almost always takes out a townie.
I think "almost always" is probably not accurate, especially in role madness games where mafia is not the only scum faction like this one could be. I can think of at least a few games since I've been here that some scum player has been lynched on day one. It's obviously mostly luck but it can happen.