Not at all. It's like a short, basic aptitude test before you're able to join a recreational sports team, or maybe a driving test. Just shows that you know the ropes at least a bit, you have at least basic competence.
Remove that and people can just bomb in on anyone's conversation in real time, from any browser, no consequences, nothing. Is that really what you want?
I object to your use of the word "elitism". Someone's basic technical competence, and the effort they've put in to do something, is a pretty reliable guide to the quality of their contribution, whatever it might be. When I see someone has a free blog on wordpress.com or what not, I instantly assume they either do not care or do not know how to set up their own system. When I see someone with a hotmail address I assume they do not know better. And on irc, when I see someone using mibbit, I assume they do not know how - or are too lazy - to set up IRC.
If people can't put in this basic effort, why let them in? You can yell "elitism" all you want; I prefer to think of it as "rules of the club". Anyone can join the club, they just have to pass the first, very easy, test. What is wrong with that?
And I think your use case for the service, as described in your anecdote, is likely to be quite atypical. I doubt the majority of Mibbit users just happened to be using it because they were using someone else's computer. You are the exception to the rule.