OK, for the pros of this method, I don't have to move hot water from my stove to a mash tun and then back to the stovetop to boil, the pot just stays put until it is time to chill. I don't have to worry about a stuck sparge so I can mill my grains finer, actually grinding them to near powder which decreases the time needed to get full conversion and reduces the need to sparge. If I want to I can skip the sparge step completely since I don't have to depend on rinsing out the sugars. I can get most of the sweet wort out of the grain by just squeezing the heck out of the bag of grain. I didn't even have to worry much about calculating the grain absorption of water since I squeeze almost all of it back out. The first few batches I calculated the efficiency and found that either sparging or no sparge gave me about 80% efficiency so the method is not inefficient.
While you read about the time required to do an all grain batch as being 6 to 8 hours, my all grain day can be 3 1/2 hours, not much more than doing extract with steeping grains. That 3 1/2 hours includes bring all my gear from the basement to the kitchen, mashing, boiling, chilling and cleanup including putting everything away in the basement again. I can grind my grains while the mash water is heating to temperature, relax for the hour of mashing since with the full volume of water in the kettle wrapped with a towel won't lose more than a degree over that full hour, pull the grain bag out and squeeze it while the water is coming to a boil instead of having to wait for the mash tun to drain and then be sparged. By knowing how my stove heats, I can just let it maintain the boil for the hour, checking occasionally to be sure it is still boiling without boiling over and spend that time sanitizing or relaxing. The hardest part for me is removing the pot of boiling water from the stove to begin the chilling. If I had an immersion chiller, I probably would chill it while it was sitting on the stovetop so I wouldn't have to deal with that hot liquid even.
The cons of this method, ....thinking.....thinking....what cons?