This has been discussed a few times here on CNCzone over the past years and you might find something if you did a few searches.
The idea is valid. It does not affect the rigidity much but you can expect some improvement in terms of reduced vibration. You are correct about concrete shrinking as it cures but there are additives that can minimize this. Alternatively you may be able to find some expanding grout mix that would work. You don't want too much expansion though.
An open mind is a virtue...so long as all the common sense has not leaked out.