Yes, it's called the navigation paradox, and it mostly came about with the advent of GPS. It's the reason we now have what's called "strategic lateral offset procedure," or SLOP, whereby aircraft on heavily trafficked oceanic routes fly zero, one, or two miles off the centerline, randomly chosen.

This is really interesting. But it seems like it could make collisions more likely, and the better solution would be separate corridors for east vs west traffic. Are there really 5 bidirectional lanes?

It's a bit more complicated than that. The routes I'm talking about are the North Atlantic Tracks, which are used for most traffic between North America and Europe. There are multiple tracks and SLOP is used within each track. All of the tracks run in the same direction at the same time, switching directions twice a day. They go eastbound at night, westbound during the day. SLOP is a mitigation to prevent aircraft in sequence on the same track from colliding. There are, of course, many other systems and procedures in place to prevent such collisions, but it's belt-and-suspenders up there.

how is it any better when 2 opposite planes choose same 2950ft?

It's not. But now that's half as likely. Several choices are even better.

I vaguely recall that planes flying in different directions are assigned different altitude buckets.