No. The situation of any phone support professional who is under management pressure to both provide quality service and filter out "unimportant" requests is untenable. The quality of support will end up sucking.
The "serious problem phone support only" thing is a nice, MBAish compromise idea that won't work well. Everyone thinks their problems are serious. The way to make this work is to provide a phone support number AND to make the web- and app-based support tools work so well customers won't feel a need to call it very often.
