However, what is more fun is competitive PvP, which is mostly unupgraded and requires almost no grinding time.
So I'm really not sure why you think grinding is an important part of Elements. It isn't unless you want it to be.
If you're just talking about straight PvP1, yeah, you don't need much to get going.
If you're talking about tournaments, league, events, and War -- the trouble is that to be competitive in most of these (and to even participate in a lot of them), you need to have most or all of the unupped cards and a sizeable collection of rares. If you've got enough cards for a few decks and a scattered assortment of rares, you're not going to be able to do much. And how do you get more money (to buy cards) and rares?... You grind. :/