Most won't.
While their bill would go up, switching means buying another phone and actually putting out effort, something most people really won't do. Most people are too lazy to even research a cell service. Which is exactly why AT&T and Verizon can charge such insane amounts.
Not to mention spending $100 on another phone just to save $5 a month means you aren't exactly going to be saving money for quite some time. 20 months just to break even, what a deal!
And I wouldn't count on better service. There is one neighborhood a few miles from me where the only service you can get is T-Mobile cellular service (no data), and usually only while outdoors. In my own neighborhood every carrier works indoors and out for all services, except T-Mobile. You can sometimes get calls indoors, but you can forget data entirely.
It just depends on your location as to how good service will be.
You're completely right about most not switching. My thoughts are that by the time they hike my price, I'll be due for a new phone since my OV is already a 1.5 years old (I'll probably wait till two), so instead of buying a new virgin device, I'd just switch and buy a phone elsewhere.
And you're right about no guarantees that T-Mobile will be better, I'm not expecting it to be. But as long as I have service at my house, I could live with it, because if there is service at my house (where sprint barely has service) then there will be service in the places I expect (like the city). I already don't get usable service in the woods and such, so having a little less pathetic service wouldn't bug me too much. Also for me, the nearest tower is at least a couple miles away and T-Mobile shows some service at my house so I assume its off the same tower which would give me comparable service. I am guessing that data coverage will be worse under T-Mobile, but since I have wifi at my house and school (places I spend 90% of my time) I can live with it.
All that said, switching wouldn't be ideal for everyone, I realize that. I may not even switch, but if they hike us, it might actually save money.