This is a reasonable summary of many of the issues organizations face only after they have started their social media programs, typically with Facebook or Twitter. Every organization experiments by adding new responsibilities to existing personnel.
Occasionally somebody gets "tasked" to do so, but almost always as an addition to existing duties. You can figure out what happens next. Organization executives are invited to help out, and that works for a little while, before the press of the business leads to waning participation.
Social media does not necessarily cost lots in terms of incremental out of pocket cost, But it takes time, and significant time if done properly.
In part, the generation of fresh content is part of the issue. A bigger issue is what happens when business partners or consumers actually start participating, or if an organization ramps up its optimization activities.
The other angle is that social media works best when lots of people within the organization are participating, and that can require a shift of organizational attitudes, support and practices that extend far beyond assigning somebody to "do it."