It depends on what your goals and ambitions are in regards to the music. Do you want to be a superstar DJ who travels the world and makes a living off the music? Then yes you need to both Produce & DJ. If music is just a hobby to take up some spare time, and your only interest is producing, then just do that (You're your own person so you can make your own decisions in life).
In the beginning of the electronic music scene, both producing and DJing were somewhat separate (Although there existed some overlap) meaning that you either DJ'd or Produced, but not both (No body cared for the DJ's back then, people only showed up for the music). With the advances in the internet and downloading everything illegally, the two positions merged as producers could no longer make a living solely on producing. (Reference - Paul Oakenfold).
As of 2015, what famous EDM artists can you list who ONLY produce, but do not also perform live? There is only one that comes to mind - Daft Punk - yet they still do live performances once or twice a year.
If you produce the next 'Animals' or what ever track that was by Zedd, then you'll do fine just being a producer.. ALTHOUGH you would be able to make a ton of money doing live gigs (And hey, if you don't want to learn to DJ, just pay someone with all that money you make to make you a flawless set in Ableton and you'll be g2g).
Hope this clarifies on the subject (OH YEAH thats the song, Clarity by Zedd)