It’s nearly 30 years since Michael Halliday first published ‘An Introduction to Functional Grammar’ and yet, at least in Britain and in the United States, functional grammar seems not to have entered the linguistics mainstream. I should be grateful for any confirmation of this from those in a better position to judge, and for suggestions why it might be so.
Before I go on with the answer I'll just point out that Hallidayan functional grammar is known more specifically as Systemic Functional Grammar (AKA SysFunc). It is not the only type of analysis known as functional - for example there is Lexical Functional Grammar (LFG). OK, now that's out the way I'll get to the answer.
I can only speak for the state of linguistic research in the USA and Britain as an outsider - I work in Australia (and for the record I am not a follower of any particular theory discussed herein). In America the prevailing formalist approach (also known as the Chomskian approach) had/has been entrenched for so long that it is hard for people to break away and start with a new theoretical position. It's not always the case — after all Joan Bresnan who started LFG was a student of Chomsky's.
One of the main reasons that SysFunc has struggled to gain acceptance is that while it is useful for looking at larger texts some would argue that it is not so useful for single-clause analysis, or typological approaches — which are still some of the main research concerns of contemporary morpho-syntacticians. Different tools for different tasks I guess!
Two disclaimers: It's been a long time ago that I read Halliday, and (secondly) I don't know that anyone agrees with me here. But to my mind, it's not a real theory. He constructs a descriptive framework which tells us how to describe languages, but not why not to describe them some other way. It's not science -- it's language appreciation. His framework is not vulnerable to counter-evidence. I find this boring.
Contrast this with Chomsky's theories. These, you can, so to speak, get your teeth into. There's plenty to disagree with and find evidence against. Now, that's fun.