The only reason Bloomberg chat is used is because all the traders have a terminal. There's no reason that couldn't be replicated. Heck, they could just get Slack. It has the main requirement, which is the log is stored (compliance). You also have group chats and "ring the bell" functions.
The thing Bloomberg gives you that's useful is a way to look at all sorts of data and pull it out in many formats. Your average trader is an amateur at coding, but he can still figure out how to pull some data onto his excel spreadsheet. Once you graduate to a somewhat more robust system, there's a bunch of APIs in all the popular languages that you can use to pull the data into your own database (are you supposed to do that? I don't know, but I'll bet you everyone does it). The data part is a bit harder to dislodge, because BBG provides a common way to refer to every instrument, and you get used to the field codes. You also understand what that data means, ie details like when the data is published, whether the numbers are adjusted for splits, etc. That would be an annoying and tedious thing to replicate with some other provider, and could easily cost you more than 20K in salaries to recreate.
Bloomberg is indeed a major overhead. If you get one for every trader/salesperson, that's quite an overhead on top of that person's salary. Most people don't event use it enough to justify having their own, but I guess they'd feel bad if they didn't have one, status being what it is on a trading floor. When things are going well, you can say "oh it's the commission on a single trade" (which is true), but when things are bad you might think twice. In order to pull all the money out of the customers, Bloomberg prevents you from using RDP into the machine.