As for not relying on power roles, that would be a welcome change. But that isn't the entire point; the point is, with No Lynch we guarantee that the detective, if any, is out there doing his or her job. The defender, if any, is out there doing his or her job. The roleblocker, if any, is out there doing his or her job. AND, there's a maximum number of potential candidates out there for them to hide in. In order for the mafia to make any progress here, they are the ones who must guess correctly. If they don't hit a detective or blocker or such, they've reduced the number of total suspects for them to hide in, and the town as a whole has gained much information.
This is why I don't argue against first-day no-lynches all that strongly despite my preferences. There are advantages to it. What I do object to is going for no-lynch as policy, right off the bat, without apparently any intention to try to put the slightest amount of pressure on anyone.

Presuming the power roles can get that information out there before they die, they provide advantages where basic townies cannot. The No Lynch strategy puts maximum pressure on the mafia.
And this is just false. Mafia face no pressure whatsoever with an off-the-bat no-lynch promotion. They're not forced to defend their opinions, they don't have to decide whether to defend or back up or ignore accusations against their teammates, they don't have to do anything. They chuck in a no-lynch vote of their own at some point and spend the rest of the time plotting in their Quicktopic. It's the opposite of pressure. I don't think a marginally reduced likelihood of the mafia making a good kill outweighs that -- that's my bias in favor of public discussion and argument showing, right there.

And really that's the heart of my objection to your post, ATPG. Not so much the voting no-lynch on day one, because despite my preferences I think the advantages and disadvantages are probably too close to call. It's not that big a deal. But doing so right at the start of a 3-day phase, backing up and giving credence to someone who had already done so previously, and hence greatly increasing the probability that the rest of the players would follow right along -- that I don't like.