Same as any security: making an attack more expensive to mount means people are less likely to try it. If high-resolution timers allow you to mount an attack in the three minutes the target takes to read a listicle page, then rounded timers require the target to keep the page open in the foreground for 3000 minutes, or 50 hours. That's much more difficult to do.

Isn't rounding pretty much the same thing as throwing away some precision in this case? So if I drop some (enough) bits and add .5 then no amount of averaging is going to recover the lost precision. Or maybe I misunderstand?

Example: You need to know how whether an operation takes 30 or 31 milliseconds, but your timer is rounded to the nearest 100ms, so you just get 0 or 100.

If you repeat the operation 100 times and time how long that takes, you should either get 3000 or 3100 milliseconds.

..and a dramatically increased likelihood of something unrelated going on in the system ruining your results. It's easy to dismiss mitigations like this as "not a solution", but at least those that add uncertainty to sidechannel attacks seem to complement each other quite nicely. Uncertainties don't add, they multiply.

I know next to nothing about the internals of how the rounding code works, but couldn't randomly choosing to round up or down mitigate this somewhat?

If you round up and down with the same probability, it will get canceled on the long run.

I suppose this does mitigate the risk a little, but risks breaking other things. For example, you don't have the simple logic sequence: a < b => round(a) < round(b)

So I'd say "not worth it"

Minor correction:

iff |a| < |b| then round(|a|) < = round(|b|)