1" thick end grain would be as stable as the wind. End grain is so finicky. A board absorbs and disperses most of its moisture through the ends. When you condense a board down to 1" long, this makes it highly reactive to change, because most of the board is end grain(think of the straw analogy). Furthermore, end grain isnt the most sound construction method for a surface. Ever wonder why the actual butcher blocks were 12"+ thick? I am no blackbelt, but if you put your 24" by 36" and 1" thick end grain board in between sawhorses, I would karate chop it in half with ease.
I make islands all the time, and I wouldnt touch an end grain project under 2" in those dimensions. I dont care how badly the client wants to value engineer the piece, that has 80-90% chance to fail, bow, sag, warp. I probably wouldnt even do 2" on a 2x3 piece. What does the base cabinet look like?
Yep, I do this all the time when it's easy to get to the glue line. When it's not I use another method. There certainly is nothing wrong with wiping wet glue. But, as with almost every woodworking technique there are some instances where another method works better or is just easier.