No point at all in putting a shallow of stores below the brood nest, IMO.
If you are expecting them to move it up - why put it there in the first place?
Bees put their winter stores where they can a) protect it - they are between those stores and any potential robbers while not clustered, b) bees leaving the cluster to feed during the winter go upwards, not downwards where they could get cooled and succumb, c) stores above the bees will not approach freezing temperatures while the cluster is giving out warmth and d) the bees will be using up unnecessary stores while moving it - both actually physically moving it and that while moving it unnecessarily they are not doing other, more useful, work.
The only plus, for some beekeepers, is convenience for them, at the expense of the bees. They usually argue that the queen will not lay in the shallow in spring - what a lame reason that is!
I occasionally place some (usually incompletely filled) frames below the brood box if the bees need a little more stores. Always done before they cluster, hopefully!
I would not normally leave the crop, just everything collected after removal of same. My bees normally stock up, afterwards, with late crops and particularly ivy. With support from the beekeeper ensuring weaker colonies are united almost always means some spare frames of stores - either to distribute late in the year or stored for use later if capped.
So, in a nutshell, waste of time and effort for the bees, convenience for the beekeeper.
