Should the polling function be turned on?
As long as it doesn’t create administrative overhead or a burden on the infrastructure. We already have polling going on so, barring the conditions in the previous sentence, there’s no reason I can think of why it shouldn’t be turned on.
I predict one of the following (usual) responses from the PTB:
[ol]
[li]It’s a huge amount of work to make the changes to enable it[/li][li]It’s a huge burden on the servers[/li][li]It will make the mods’ job much much harder[/li][li]It goes against the culture of this place, and it will make it unrecognizable[/li][li]It will cause the end of the universe[/li][/ol]
Should we take bets on which one it will be?
Too close to call. 
Yes, it should.
#1 & 2 are still the most likely.
#3 is unlikely. Moderators already have to manage the existing polling threads. Enabling the polling feature shouldn’t change the moderating burden.
#4 makes no sense. As I pointed out, manual polling is permitted so why not enable the mechanism that helps streamline the process?
This would be my concern. If turning on polling doesn’t make the board response even worse than it already is, I say, Yes, turn it on.
The other items in your list I don’t think are really issues. (Except for the end of the universe one - is the Large Hadron Collider still down? I’d worry about the interaction between that and the board.)
Yes please. Every other vBulletin board I visit has it turned on, and it’s useful.
We’re talking about a message board where much of the staff and userbase are against adding new smileys. Think we’ll get polling? I’d respond with the LOL smiley, but there isn’t any.
I support the polling feature but oppose new smileys. So there.
Polls belong in IMHO . . . not here.