It’s frustrating just reading through this.
However, I’ve personally never found it necessary to email them directly. If you have any special requests, you can have your concierge contact the hotels for you.
I see a lot of businesses making it hard for customers to contact. Their “misguided” reasoning is that if it’s easy for them to contact you, you’ll be flooded with messages. A lot of businesses also don’t staff enough to respond to their customers. So in response to staff complaints of workload, they just turn off the tool itself.
That said, having been on this and other forums, I’ve seen plenty of requests for GM emails. I can’t imagine how many emails the GM must get for frivolous requests. Maybe that’s why they don’t want a first name.last name @ Hyatt email address.