Consider a reactor that consists of two colliding beams. Should work great, right? Well, the reaction rate is minuscule, so you're wasting a whole bunch of energy in the ones that don't collide. It's a numbers game; in the sun there's a process that has a reaction rate of something like 1 in billions of years, but it's okay because there are orders of magnitude more protons in the sun.
The point of tokamaks and stellarators is that the field lines are closed, and you won't have leakage out of cusps like in mirror machines. You prop up the energy distribution with techniques like neutral beam injection and electron cyclotron resonance heating, since the ions tend to dump their energy to the electrons.
In other machines, mostly inertial confinement devices, the claim is that a pulsed mode of operation will be effective. However this remains to be shown, and some work (see Todd Rider's PhD thesis) claims to prove that such non-equilibrium schemes cannot reach breakeven.
What's especially nice about thermonuclear fusion is that it's feasible that the fusion reaction itself keeps the plasma hot enough.
> this means the vast majority of collisions will just send your ions pinging out of the magnetic bottle they are in
Here's the thing: collisions get less frequent the higher in energy you go. This seems counter-intuitive, but consider that the vast majority of "collisions" are actually weak Coulomb interactions at a large distance. If you're approaching an ion at very high speed, your trajectory is not deflected very much.
So while collisions are a major concern in stellerators in this sense, they are less so in tokamaks, where turbulence is the main limiting factor.
[1] By those smarter than me, that is. It's incredibly complicated.