Some napkin math - total Internet bandwidth is estimated to be 3-4 petabits per second. Let's say 1% of that is inference traffic - 35 terabits - then that's ~4.375 trillion characters per second at 8 bits per character. A single keyboard press might require 2 mJ, so you need roughly 8.75 GW (electricity required for ~9 million homes) of continuous mechanical force to keep pace. This would cause the keyboard to heat up 175 million degrees C per second. Disappointingly, this is not enough to create a black hole but I'm sure Randall Munroe could tell you how the guy's pet T-rexes would be vaporized into previously unknown types of plasma and how satisfyingly whimsical that would be.