Ah, but you must remember, mass is conserved. Your water does not disappear into the air... well, a little bit of it does but not enough to matter... it remains where it melted and starts acting like a liquid. So what does it do? It runs down things. Until it drops back below freezing. Which it will. Your gutters rapidly fill with ice, and the water is now all over the siding (which really doesn't like ice that well), all over your sidewalk, all over your car... it's much less of a solution than you might like.
I live with a moderately steep driveway facing onto a moderately steep and short road, with me having to go uphill to get out of it (dead end otherwise), and I have to admit I've entertained the idea of melting my driveway off in a similar manner, but only because I'm a bit darkly amused by icing the entire rest of the road so nobody below me can get out, even with four wheel drive. I suspect local law enforcement would find a reason to fine me, though, and they'd be very right.