afterwards, someone comes up to you and says something like "great gig, really liked it. You need a different drummer though, I didn't like what he was doing. Hey, I play drums, I could do it!" Or if you're a solo act: "That was awesome, but what you really need is a bass player..."
What's the point in this? If it sounded that great, then the offending member clearly doesn't need changing, and the band is probably hapy how it is.
Why do people try and offer their services?

people open their mouths
flap them up and down and crap comes out. my life has never improved as a result of someone speaking to me. that's why i've stopped inviting any comment whatsoever and become a hermit.
"what you guys need is...
a real drummer"
then we'll be a "real" band apparently.
mostly though people say nice things, it's just a few randoms who annhilate our band by suggesting we get a drummer or singer or bassist, because apparently you can't make electronica without a drummer, singer or bassist.
constructive criticism I guess...
I'd always be up for hearing feedback off people who'd taken the time to watch and enjoy a set of mine/my band...even if you don't agree with it, at least it means they were paying attention!
Constructive criticism I have a LOT of time for
It's the only way to improve...
But when it's blatant "get rid of this person so I can replace them" nonsense...
On the other hand, has anyone actually taken someone up on an offer like this, and if so what were the results?
Same reason that my club night
that doesn't put on bands is inundated with bands asking to play who then get stroppy "Oh we're not good enough for you eh we played xyz the other day" when we tell them we don't put on bands.
People are self serving belters