Cooling, lubrication, debris removal and dust control. Mostly in that order.
But yeah, you're completely right about the chisel. Hammer and chisel is how we've processed rocks for most of history (all the way back to flint knapping).
Wet processing for tile/stone is really only about 100 years old, since we didn't have a usable cutting abrasive until diamond blades came around in the late 1800s.
---
All that aside, the problem with a hammer & chisel is that it's hard to be precise. It's not impossible, but it's definitely a skill requiring mastery.
If we expand the scope a little and include ceramics - then yes, we did need quite a bit of water.
Brick, Clay, Cement, etc - they were all good alternatives to chiseling stone to get a very hard, stone-like material in a very specific shape, and they all require good amounts of water.
>The models estimated that Oldowan stone tools originated 2.617-2.644 million years ago, 36,000 to 63,000 years earlier than current evidence. The Acheulean’s origin was pushed back further by at least 55,000 years to 1.815-1.823 million years ago.
These days, with high-power cutting tools also for cooling. If you have a 50 HP saw, that energy has to go somewhere, and it doesn't all go into the dust and get carried away. If carbide blades get too hot, the solder melts and the brazed inserts fall out, and for steel, carbide and diamonds, the hotter they get the softer they get and and the faster the tool wears.
And other than the cost of the tools, there is one thing harder to drill than a rock, and that's a rock with the previous drill bit's carbide insert stuck at the bottom of the hole!