It does make sense, it is quite useful, but unfortunately, without being rooted, it's not possible in an easy, built-in way.
You can "mirror" your phone on a TV (or a PC/Mac monitor with HDMI input) via an MHL dongle; basically this connects to your phone via microUSB and converts video/audio to an HDMI output. Just watch out! MHL connectors for Galaxy S2 and before are NOT compatible with newer MHL adaptors for Galaxy S3/Note 2.
You can also "mirror" your phone's screen if you own a Samsung SmartTV via AllShare Cast. Now this is where I don't get why... AllShare Cast is a software feature; you can download Samsung's Kies to your PC/Mac and use all the AllShare features EXCEPT the AllShare Cast screen mirroring...
Finally, your last option (and the best you could do unless you're rooted), is to use a VNC program. These programs let you "see" your phone in your computer and manipulate the contents you're seeing. You need to have the software in your computer and a client in your phone. Most ones are not free, however.