I've rarely had a problem getting (or figuring out) a GM's email address. For Starwood it's first name.last name @ starwoodhotels.com about 99% of the time. I assume that as the senior manager of the property the GM is in the best position to direct my mail to the right person/department. I don't worry about whether there's another way to reach the property manager because email is most convenient for me. I also suspect that many (most?) hotel GM's have someone screening and distributing their email, and as noted below, it takes almost no time - certainly not 30 seconds - to forward an email to a staff member.

These days I almost always use email to communicate with hotels: it's easy and 'on the record'; I only call when I'm looking for information or a transaction that I need to complete immediately. Works for me, and works for the property too; I have never heard a property manager say "we would rather not get emails about good or bad service"...