I worked at a small company where Engineering rotated through support. There was some value in it, but also it sucked doing it and there were other companies out there with interesting work, good pay and _not_ asking you to do support. It was absolutely part of the reason I left.

Admittedly the company was small and you were doing support a lot (up to one week a month depending on team). Something more like one week every six months would have given you the customer visibility benefits without all the engineers absolutely hating it.