It boggles my mind why one would cut holes in a device rendering its purpose useless. This logic is likened to poking a small nail into the side wall of the tires on the truck to make a slow leak because they hold too much air on a hot day. Then being upset that the tires are flat next weekend.
The idea may work if you are running weak colonies in double deeps. If you are running singles, good healthy hives, in warm weather; you can be quite sure that she?s going upstairs within a week after the corners have been cut out. I say this because in peak brooding period the bottom box, run as single, is wall to wall brood. A good queen going hard and constrained will lay levery cell available. She will find the corner openings herself or the bees will usher her through them.
The QE is not a standard or necessary piece of hive equipment. It is a beekeepers TOOL that has a very specific purpose. That is to enable the beekeeper to manage the broodnest location. You either want to manage the queen and where the nest is or you do not. Do not be half baked about it. There are also other methods to managing the nest. Though the QE makes it easy.
The QE has no end effect on honey yields. If the bees are not putting the nectar/honey above, it is because they do not really need the space or the setup is not encouraging to them, yet. For example a box of foundation plopped on top of the QE is not going to get much, if any, attention until the lowers are completely filled to capacity. However a box of drawn wet comb above the QE will be immediately jumped on and worked as one with the rest of the combs.
All that said, the type of QE and foundation makes a difference. Big bees from large cell foundation have a difficult time squeezing through those small poor quality plastic queen excluders. Know each piece of your equipment and ensure it is compatible with how you operate. Know the foundation size and use good quality steel QE.
Finally, in the heat of the summer and heavy flows there is benefit to a top entrance. This is as simple as offsetting the top super forward by 3/4?. The bees will appreciate it. Has nothing to do with the QE. It is about reducing the walking distance they have to go to get to the door to go get another load.
Cutting corners rarely gives sustained positive results. Usually doing so blesses you with unintended alternative results.
IMHO