Bloomberg operates a group of distributed, redundant data centres with massive compute and network infrastructure to ingest real-time data from every exchange and major market participant in the world, across a huge range of financial asset classes. It then fires the tiny subset of this that you happen to be interested in at any given moment down to your Bloomberg terminal.

In addition there is data that only they have because it's generated as a by-product of their trading functionality. If I'm MegaBank Corp and I want to sell e.g. credit default swaps denominated in Norwegian Krone, I can advertise this by feeding my prices for such deals to Bloomberg so potential clients who also have a BB terminal can see them and click a price they like to make a trade. This gives Bloomberg a pool of liquidity/price info that no independent source has access to.

So there are very strong network effects. Even if you could spend the billions to duplicate the infrastructure and rewrite all the software required, to actually do the same thing you would also need to replicate all the business relationships with data sources.

Disclaimer: I am not a lawyer/cat/financial-advisor/etc, but I used to be a developer at Bloomberg :-)