Conical burrs deliver a different shape of particles compared to flat. They tend to drag and break the coffee and the flat break and cut more than break.
In grinder comparison and laser analysis diffraction the conical and some flat (this is geometry-rpm related) tend to do more boulders than other flat grinders.
Let's say we want to grind for espresso, and we know that for a traditional espresso we grind between 200 and 600 microns. In this range we are going to get the highest percent of grind particles. But some grinders deliver a high percent over 600 microns, up to 800/1000. Those are boulders. I am grinding finer than 200-600microns.
Now from a discussion and a presentation of Perger we know that water penetrates totally up to 100microns in the walls off coffee particle, watch this video and if you want to see the explanation about this watch after min 34 : http://www.youtube.com/watch?v=2lPGf1gM9nA
If we draw a circle with 100 micron radius we get a perfectly rounded particle with a 200microns diameter. That will be fully wet and extracted. For high extraction yields you need to grind fine and the distribution needs to be uniform, because if you have fines that will lead to choke, and if you have boulders that will lead to under extraction. Fines will lead to under extraction as well because water will be forced to find way out and do micro channeling.
There is another thing involved, the shape of the particles influence the hydraulics and how the water flows. A puck made out of square and angular bits will have more porosity and permeability than a puck made out of "flakes". The grind from flat looks similar to flakes. So the flaked coffee puck is harder to extract and in most cases people will say they have more channeling with a flat burr grinder than with a conical. Or I hear a lot my Kinu is way better than was my Lelit flat grinder.
To achieve higher taste or EY you need good coffee (air roasters like Loring will roast more even from inside out this means you can extract more from the volume of coffee, if the bean is undeveloped in the interior that will not allow you to extract) a flat grinder that has uniform grind and a flow/pressure profiling machine that does what you say (temperature, flow/pressure, time-stops-starts).
We humans like to over complicate things, we are curious and always search for more, it is never enough. Some may say what the hell! why would you buy almost "green" roasted coffee and try to make espresso out of it, remember this is a hobby. This is time consuming, a lot of money involved. Getting the last 5% out of anything is like this, I don't know if it was worth it.