I thought the original idea was that it was supposed to 'accentuate' her being non-human, more than anything else. The real problem isn't with Deanna's dodgy accent, it's with the fact that Mrs Roddenberry made a mockery of those original intentions by playing Lwaxana with her regular voice, which is what forced the aforementioned line about Deanna's father into the episode to cover Majel's apparent unwillingness to play along and do the strange accent. And then, of course, every Betazoid that followed Lwaxana just used the actor's normal voices, too.
I agree with the general consensus that Marina using her 'real' voice in the movies was much better. In fact, one of the weirdest things for me about the finale of Enterprise
was hearing her using her TV series voice again (she kinda sounds like she's forgotten how to do it, but at least she does try).