It's every ten minutes - quicker than going miles out of your way (unless you're Hippy).
As for the £3 - well, I can't imagine something spanning the river at that point, which would have to be either very high or openable or both, would be financially feasible without some kind of toll.
Yeah but that costs £3 a pop. And isn't that frequent. Or open at night.
RE Rotherhithe tunnel. Done it twice. Never again. I like my lungs.