I used to work on Gmail anti-spam. Blocking attempts to send spam through the browser UI was most of our job. Driving browsers by things like AHK is (a) detectable and (b) definitely slower by more than an order of magnitude! You can much more easily run many requests in parallel (through proxies) within the RAM budgets of ordinary desktop/laptop computers, when going direct to the network. You don't have to believe me, go read spammer forums to see people discuss how much better multi-threaded bots are.
"the enterprising spam sending people would still easily automate the browser, esp. with things like autohotkeys"
It's not at all easy for them, and people who try approaches as simple as that don't make any money. Or didn't when I worked on it at least.
"The point is, banning a client side mod for any service is irrational if the justification is to prevent spammers."
That belief is widespread, but I built a part of my career on proving it wrong. We got unexpectedly excellent results from cracking down on alternative clients that were pretending to be browsers.