I disagree with you and I suspect it will be used by more than a few traders as an indicator of sentiment - they'll use it a way to quickly gauge what people are thinking about particular companies and use that as another variable for their trading/sales decisions.

Your two reasons don't make a lot of sense to me, based on my experience in the industry. Specifically -

(i) If you're using a Bloomberg terminal, it's somewhat implicit that Bloomberg knows what you're using it to look at (as well as who you're emailing via it etc). If people didn't trust them not to tell everyone else what you're looking at, no one would use Bloomberg. Your strategies shouldn't be a secret from the rest of your desk or your own company (assuming you're at a bank/hedge-fund/prop-house rather than a rent-a-desk prop-shop where everyone only works on their own accounts and thus the guy next to you is your competitor). The majority of traders aren't executing their own strategies anyway, but are working within a set of parameters set by their company or clients.

(ii) a) This is becoming less true, more and more banks etc. are allowing access to view Twitter, but not to post to it. b) I think you might have missed the point of the service where Bloomberg is offering a read only Twitter feed to avoid the problem of Twitter being blocked.