I don't think that the cart will move forever, though.
You're basing that on real world physics, not on DF physics. And even in the case of real world physics, you're not comparing it correctly. I'm not sending the cart up one hill and back again. What I'm doing is sending it between two actively powered boosters. Boosters are called rollers.
>=^<
> Roller pushing east
= Bridge
^ Plate
< Roller pushing west
Rollers are powered by mechanical power and axles and gears. That means water coming in from the river is powering the rollers. The cart hits one roller, and is propelled forward over the bridge and plate to hit the other roller, where it's stopped and sent the other way. Each "push" is a unique action and not influenced by the push before it. Every push will have the maximum energy that a single roller can impart.
When you want to disengage the latch, you pull the lever on the bridge, which causes the cart to fall out of the system and allows the plate to reset.
If the cart moves back and forth quicker than 100 ticks, then the plate stays down. In other words, it has 100 ticks to hit one roller and get pushed in the other direction. If it takes shorter time, then it "resets" the plate's timer and keeps it depressed. It it takes longer time, then it allows the plate to trigger and you end up with a repeater.