Not convinced, for small amounts of smt ic devices it could be nice.
But most of my smt products will be larger than those storage containers (elco's, coils etc) and they differ in amounts, from some I have ten pieces which will be ok for these drawers but from others I have complete reels of 2000-10000 pieces, not very handy to split them up.
I use an Excel sheet for all my smt components , amounts left, interesting specifications (capacity, voltage, ripple current etc. etc.) and I also put a link to the datasheet that is stored in the SVN repository.
If we are going to automate it then do it all the way, a robot like found in pharmacies that pick the right drawer, open the package and take out the amount of pills requested and returns it.
That would be neat, upload the BOM and get a esd safe container with all the requested stuff in it, oh well dream on