I just used Hyatt's Twitter DM feature to contact the Hyatt Concierge service. I booked a room using points on my own via the web. Then I used Twitter to DM Hyatt Concierge and provided them with my Glob # and confirmation number. I asked them if they could confirm a suite upgrade award to my reservation. I timed the response......6 minutes and 20 seconds later they responded saying the suite is available but would need to call the hotel to confirm and asked me to reply. I responded to proceed. 10 minutes later I received the Twitter response confirming the suite upgrade with the property. They always have to call and confirm so that takes some time and depending on time of day your mileage may vary.
So in summary, delays from the MHC team has to have context. If I were a newbie Glob and sent in this request over email to MHC that wouldn't make any sense. The bad part is the MHC email team is not doing triage to the emails to respond quickly and redirect requests for the most optimal execution.
I think MHC is probably getting a bad reputation because nobody is being coached on how to best use it. That is on Hyatt to do!!!! Set expectations accordingly....