> Genuine counter-movements (e.g. grassroot preferences) might not be as leveraged

Then that doesn’t seem like a (counter) movement.

There are also many “grass roots movements” that I don’t like and it doesn’t make them “good” just because they’re “grass roots”.

In this context grass roots would imply the interests of a group of common people in a democracy (as opposed to the interests of a small group of elites) which ostensibly is the point.