Current is pulled, not pushed. If too much current is getting through the resistor, it would be because the IC is pulling the current, which means it's already in trouble. My guess on the in-line resistors with the IC power pins would be an extra LPF for the power rail of each IC, in which case the exact value of the resistor isn't super important as long as you're getting close to the right corner frequency on the filter.
So is this to mitigate high frequency power noise/oscillation (I thought the caps did that)?
Not necessarily high frequency, but any ripple/noise that could be in the lines. It's not as common in audio as the ICs aren't that sensitive and the bulk filtering on the input is generally sufficient, so in something like a pedal it's overkill in my opinion. In more sensitive circuits it's common to have a ferrite bead (or resistor) for each IC for an "isolated" filtered power rail.
I knew that didn’t make sense
