Obviously. But I was responding to "what is sinister about a GET request". To put it a slightly different way, it does not matter so much whether the request is a read or a write. For example DNS amplfication attacks work by asking a DNS server (read) for a much larger record than the request packet requires, and faking the request IP to match the victim. That's not even a connection the victim initiated, but that packet still travels along the network path. In fact, if it crashes a switch or something along the way, that's just as good from the point of view of the attacker, maybe even better as it will have more impact.
I am absolutely not a fan of all these "are you human?" checks at all, doubly so when ad-blockers trigger them. I think there are very legitimate reasons for wanting to access certain sites without being tracked - anything related to health is an example.
Maybe I should have made a more substantive comment, but I don't believe this is as simple a problem as reducing it to request types.
Get parameters can be abused like any parameter. This could be sql, could be directory traversal attempts, brute force username attempts, you name it.