Mycroft trusts few people. He trusts his employees and coworkers to do their jobs (at most). He might trust his friends if he had any.
He trusts Sherlock.
Many people wouldn't. They might trust him to know the answers or to be honest whether they wanted to hear the truth or not, but if their life depended on him dropping everything and coming to their aid, they would be skeptical.
Then again, Mycroft doesn't trust Sherlock with his life either. Because as much as he resents him, as little as they get on, Mycroft still sees him as that bundle of lanky bones topped with a black tuft of hair his parents placed in his arms on a cloudy morning in his childhood. That bundle is really all he has left that means anything at all.
He cares for Sherlock as much as he is capable of caring for anyone. And Sherlock cares so little for his own well-being. ("Breathing. Breathing is boring," he has said.) Mycroft is afraid that, one day, he will get that call, and what is he to do then?
So Mycroft is actually grateful when John refuses payment to spy on Sherlock. That, as well as everything he had seen of him before that point, seemed to indicate that this man was going to take care of his brother. All evidence following that just confirmed it: he shot a man who would have killed Sherlock; he interrupted his date to intervene in Sherlock's fight with a Chinese hit man; he offered to let himself be blown up if it meant Sherlock's life might be spared.
Dr. John Watson was a military man for the same reason he was a doctor: his natural instinct was to take care of people. And this predisposition increased when he cared for a person.
Sherlock's life was never safe. Mycroft did what he could (quietly) to help make it so, but he knew his brother needed constant watching that he wouldn't accept from him even if he could offer it.
John was the perfect solution. He couldn't have planned it any better if he'd tried.