The big push for LTE, and faster data speeds, is simple; Cloud Computing, Streaming Video, Online Gaming, VoIP, Video Calling, and I could go on.
The problem lies as technology grows, the demand for faster speeds grows with it. Remember when 28.8 Kbps modems were around. No one ever complained, they loaded internet pages just fine and the local AOL chatroom. Then digital cameras took off, 56K was introduce, and webpages started hosting larger content (i.e. pics, small low quality videos; real player)
Now you have services like dropbox, while HSPA+ networks are sufficient to some degree, you have people like Apple, Google, Amazon, all pushing for "Cloud" computing.