Good lateral thinking but
Fisrt, you go forward to get a towel
Second, you go aft to get a bucket and line out of the lazarette, assuming the galley sink is not accessible or the pressure water not on
Third, towel overboard in bucket
Fourth, return to galley...
Even if you grab a wet towel from the settee you're giving the fire too much time. A fire's size doubles every 30 seconds and if it is behind the stove, etc., you don't want to start looking and thinking.
There really are fire blankets, they are not expensive. Aramid or kevlar, yes, pricey, plain old cheap tight wool blanket will do equally well. It really should be in a box, wall mounted and ready to pull and use, if you plan to use it. The extinguisher allows you to keep a little further back from the flames though, so it might still be worth the mess.
People tend to hesitate to use an extinguish, for a number of reasons, and that time is critical. A cool headed person instinctively uses a blanket or something equivalent where appropriate; they quickly remove any nearby fuel and then smother the fire. I've worked around combustion testing labs and welding a good bit, where puting out little blazes is commonplace and reflexive.
I'm sure I can wet a towel in less than 10 seconds with less ritual (
); several always hang near the companionway (cats are broad there) and I have steps on the transom. Most cooking is at anchor, if that is the example.
I like the fact that a blanket tends to confine the flames; in addition to the mess, extinguishers can knock things about.
I'd forgotten fire blankets were wool when I was a kid. Almost a reason to carry one.
I like the idea of a kitchen towel that could be dual-purpose; very flame retardant and a bit larger than typical for a hand towel. An idea for the chandlers listening at the edges!
But there's nothing like a good ol' wet blanket!