Can one put a group of layers into independant precomps?

It would be possible with a script, but it has to be done carefully.

There is a layerCollection.precompose() function but it uses the index number of the layer(s) to be precomposed (the number shown next to the name in the timeline panel). Since every time you precompose a layer, the numbers will change, the script has to work from the bottom up. The act of precomposing also resets any selection, so if you're using that rather than something like label colors to choose your targets, the script has to cache their numbers.

Here's a very basic script that does that. I assume you have the composition selected in the project panel, and the layer(s) selected in the timeline - and that the layers make sense to precompose in isolation:

var moveAllAttributes = true;
var laycol = app.project.activeItem.layers;

// first cache the array of layer selections, starting at the bottom
var selectedLayers = new Array();
for (var i=laycol.length; i>0; i--) {
    if (thislayer.selected) selectedLayers.push(i);
}

// now precompose them individually
for (var s=0; s<selectedLayers.length; s++) {
    var thislayer = laycol[selectedLayers];
    var precomp_name = thislayer.name;
    laycol.precompose([selectedLayers],precomp_name,moveAllAttributes);
}