Exactly. I enjoyed using minis much more back when we played 2nd Ed, when they were merely colourful visual representations of the approximate positions of the characters, not surrogate chips on a wargaming board. Sadly, I recently played in a 4th Ed game where the DM refused to let us use miniatures, insisting instead on using counters, because it was easy to put buttons on them to indicate who was marked, etc. Sigh.The last thing I care about is what square is character X standing in. After all, the space the action takes place in isn't actually gridded so why have the players obsessed over the area as if it were?
For instance, in the first post in this thread I mentioned that how the response of my players to the freaky roof climbing baby was to assume it was 'Spiderclimb'. I was hoping to elicit a sense of supernatural horror, but all the players seemed to witness was a spell effect. It brought home to me how 'unmagical' magic had become - in a world filled with magic, magic was no longer special. Ultimately the myriad list of spells had made the world a smaller place, where magic was all mapped out. It felt like there was no wildernesses left, no place on the chart where the only label was "here be dragons". The lack of frontiers was killing the sense of wonder.
Keeping standard D&D magic in play and still producing that sense of wonder requires there be a magic behind the magic. A wild type of magic with effects unexplainable by the "normal" laws of magic. The laws that govern this magic don't need to be balanced in game terms since it is important that the players never discover how this magic operates.
Alternatively, how that magic works can be one of the things that drives events in the world, such that the characters have to learn it - by the end of the campaign they've figured out enough to deal with the situation. The magic is slowly peeled away over time, but by the time it is fully exposed, the game's done.
I do almost the same, but I use the back side of desk calendar sheets and have to draw my own grids on it (using a pencil and a yardstick) before getting to the details of the given battlemat.My solution was to buy a few big sheets of poster sized graph paper and draw battlemats ahead of time.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.