Does it really enhance your experience *that* much when all is said and done?

Yes, it does. I know I'm a minority in the fanbase, but I have very little interest in 20 minute + jams, no matter what the song is. What I want to hear is the band's written compositions and songs played really well. I've had two experiences with a bustout at a show I've seen:

Pebbles & Marbles 8/7/09 The Gorge
Scents and Subtle Sounds 9/2/11 Dick's

Those are two of my very favorite Phish songs and both of those versions were rusty as all hell. They've never been setlist regulars so when they did bust them out in a period where they weren't the "practice 8 hours a day" Phish of the early 90's, it was painfully obvious.

Is it really terrible if you got a killer jam out of a Tweezer instead of, say, something as rarely played as Lifeboy? Or, hell, even more commonly played songs like Fee or The Mango Song?

Not a great comparison, I'd say. Tweezer is a setlist regular and it's expected that there will be a jam. Lifeboy, The Mango Song (two more in my Phish Top 20) and Fee with a few exceptions aren't jam songs, they're played pretty much straight-up. Again, I'd rather hear the two songs above and the three just mentioned than a boring 24 minute version of Rock and Roll that I heard at the 8/15/12 Long Beach show. It was hilarious to hear people after the show and later online be all "OMG! A 24-minute R&R, awesome!". The fact that the jam went nowhere, almost ended completely after about 13 minutes but then noodled on for another 10 doesn't seem to matter.