Hello :)
The use of deliberately non-standard English gives a great deal of power to this statement, for two reasons:
- It makes the sentence stand out. If I am speaking ( as I usually do!) in correct, grammatical, standard English and I suddenly say 'If it ain't broke, don't fix it', this is a linguistic signal that these words are different. It makes it obvious that I am using a figure of speech/quote/cliche/set phrase of some kind, and it is immediately clear that these are not 'my words'. It's a signal that I'm using a sort of metaphor to illustrate my point, rather than a neutral statement to be taken literally.
2. As Paul says, the choice of grammar which sounds unsophisticated and old-fashioned reinforces the message. The use of this unpretentious language seems to hark back to an older, simpler era when basic common sense was what counted most. We say this expression of 'If it ain't broke' as an encouragement to use common sense, and the language it uses does a lot to strengthen this message.