Getting the same feedback from our team. Do not like that they have two systems to check. What we setup was when I tech was not available (either outside their scheduled working times, or on vacation), the ticket was routed to the Group Manager. We setup a Tech called Alert Central and made that tech the group manager. Web Help Desk sends the e-mail to the address we setup for Alert Central. A source rule in Alert Central reads the Web Help Desk e-mail looking for key words (like Request Type) and then picks a group and user from the group's calendar.
What occurs is Alert Central sends the e-mail with information from the Web Help Desk e-mail. The assigned user (tech) then needs to acknowledge the Alert Central request, then sign on to Web Help Desk, find the ticket and assign that ticket to themselves. Now this doesn't appear that much of a burden, but when you are asking people to do this while out of the office, at home, getting woke up, etc. I can see the pushback is valid.
If integration between WHD and Alert Central is not possible, (it is isn't it?), I would like to see adding an On-Call checkbox to WHD. At least then with this in place, an algorithm could be setup to collect all techs in a group that are on-call and make the assignment to one of them (round robin or load balance). I have put in this suggestion as a feature request.