Grinding, twisting, coring the chalk is not the correct way to apply chalk. Go read.
I've read. I brushed for years. I then noticed the people who were destroying me at the table gave the chalk little attention. They applied it from their palm every shot with a half rocking, half grinding motion without ever looking at the chalk/tip. Yes, it creates a mess. I clean my table, my buddy cleans his table, the place I play $5 tournaments cleans their table. The thing is, the mess is minute compared to the the effects of losing concentration even for an instant while playing. I'll happily half rock grind (not over the table, I'm not a barbarian) rather than risk a tiny bit of distraction and loss of visual focus. Bonus points if my chalking causes my opponent to lose concentration. If he/she gets a little blue on their hand and can't handle it, maybe they should get their own table and dwell in the basement only. I learned long ago to not worry about how my opponent chalks, strokes, stands, etc. Much better to focus on the table layout than be distracted by something that has no effect on your personal performance. Unless you're super human or on the spectrum you only have a finite amount of focus, best to keep it reserved for things you can actually control.
In all seriousness I get what your saying and I get why you brush instead of grind but I'm not going to mentally sabotage myself worrying about how I apply chalk in a match, as long as it gets applied every shot.
Watch SVB, a dude who none of us here can match. He grinds in game, not like he's starting a fire, but a chalk in the palm, half twist rocking motion. This is how I do it. The act of chalking shouldn't interfere with your visuals. The only way you're getting an even coat with brushing is to look at the tip. If you know how to properly "grind," more of a rocking motion, you don't have to take your eyes off the good stuff. Ask yourself why all these pros are so dumb to not even know how to properly chalk? Maybe the whole "correct" way to chalk isn't as important to your game as we've been led to believe. I remember reading it in old pool books, I remember fats telling us he can spot someone he can beat by watching them chalk. I'd take SVB over fats in an even match any day.
I'm generally frugal in life but I'm not risking an "L" over a 25 cent cube of chalk.