The issue that I have with the "allow the player to measure out the distances" concept is that the Wizard is able to be totally accurate, whereas all of the other PCs and NPCs have to roll dice to see if they hit.
I have no problem with a player saying "I place my Fireball here" and that is where it goes.
I have a problem with a player attempting to measure this out to the nth degree.
My PC got hit by friendly fire just a few game sessions ago. The DM asked which intersection the player of the Warmage was targeting his Fireball, and then we figured out who got hit. My PC happened to be just within the radius.
In fact, we recently started using metal templates that the DM made to figure out exact location of area effects like spreads and cones. It makes it pretty easy to just drop the template from above over the miniatures.
However, people who do not allow the players to make such mistakes are missing out on a fun element of roleplaying.
My PC and the PC of the other player had a serious discussion about targeting friends and foes. "Sure, it's good to damage multiple opponents, but unless the situation is dire and we will lose unless you do so, damaging an ally can also lead to dire situations".
That type of conversation won't happen in a game where the DM allows the players to measure out exact distances. An entire aspect of roleplaying is lost when you do this. And to me, it is no different than having a player move his PC through the squares and the DM saying "Ok, the Troll gets an Attack of Opportunity against you for moving through that square." and the player saying "Oh, in that case, I take this different route." and the DM saying "Ok".
Playing that way is like playing a computer game where your offensive spells do not affect your allies. Boring and lacking in plausibility (i.e. it reminds you that you are playing a game as opposed to you just experiencing the game).
People make mistakes. Oh well. If you are going to prevent that at all times when possible as a DM, why are you playing the game?