There's no legal obligation to set up a breakup fee, and it's not specific to the US; it's a conventional term in potential merge agreements when there might be an expectation of regulatory interference.

The announcement of a merger has major market effects, which tend to improve the standings of one company and not the other; the announcement of that merge failing will have similarly large market effects. The breakup fee is simply a term in the negotiated contracts that specifies what happens if the merge fails to go through; the company whose market standing will fall as a result of the merge failure would negotiate to get paid a breakup fee.

It's just what they (Sprint and TMO) have agreed to.

Short answer: Because they agreed to.

There is no special law or anything covering it that I'm aware of, it's just that T-Mobile says "This will be a distraction, and there is serious risk that it won't happen. If you want us to take that risk, give us some insurance"

Apparently Sprint wants this deal badly enough to risk losing $1B if it doesn't go through, and T-Mobile was canny enough to realize this fact and negotiate for that clause in the contract.

Potential mergers and acquisitions take up a lot of time and resources on both sides -- gathering information, legal fees, meetings, etc. Plus, due diligence is a huge distraction from the normal course of business. The breakup fee protects T-Mobile in case the deal falls through. Smart move.