Your modification to the analogy is wrong. You're taking a fair scenario and changing it to be unfair. In your version you end up pouring less overall volume of water into your glass compared to the drip side. Your scenario forces the drip side to slowly overflow, but then you say, "well, I control my side and limit my pours so the glass never overflows".
Well yeah of course you can control how much you pour each time so you never over flow. But I can ALSO slow down my drip rate so it never overflows. So what's your point??? You are allowed to control your pour rate but I'm not allowed to control my drip rate? What the hell?
It’s not my fault it’s a poor analogy. Although I’ve explained the real world situation several times and it is easier to understand as well as more valid, here it is again:
Let’s assume the heat input is the same for both dragging brakes and pulse braking. With constant braking the heat is put into the system continuously and is radiated away continuously. The heat build up is linear and additive. The longer the brakes are rubbing against the rim, the more heat goes into the rim. The radiation of the heat is also additive but, since it has a negative sign, is subtracted from the heat input. But the constant input of heat never lets the radiative losses out pace the heat input. The temperature of the rims increases as a result. (Heat and temperature isn’t the same.
This link explains why.)
With pulse braking, the same amount of heat put into the rim but there are intervals where there is no heat being put into the system and heat is being removed from the system. No heat being added and heat being subtracted results in less overall heat in the system. The temperature of the rims doesn’t increase and may even decrease over the same distance traveled.
The pro cyclists are descending at nearly 100km/h. Air resistance increases at the square of the speed. It's an exponential increase. At those speeds almost all of the gravitational potential energy of the altitude is being burnt off via air resistance.
And the pulse braking system results in a higher overall speed as well. If you are dragging your brakes, you are trying to keep your speed down over a given distance. And, yes, air resistance comes into play at higher speeds as well. Someone practicing pulse braking can take far greater advantage of the wind resistance and wind braking so that heat doesn’t go into the wheels as it does with constant braking.
The pro cyclists barely tax their brakes at all. That's why their brakes don't over heat. It has nothing to do with pulse braking.
Sorry but that is incorrect. They tax their brakes (and rims during the age of rim brakes) far more than us regular cyclists do. They brake harder for corners than we do and they are traveling at a higher speed. Their brakes don’t over heat because they don’t use them all the time. They don’t drag their brakes down hills to control their speed. They brake hard for corners and then let the bike fly. If they need to control speed in straights…not something that happens very often…they tap their brakes, slow a little, and then get off their brakes again. That is the very definition of pulse braking.
If they tried to drag brakes down a hill, they would lose.