Except it is not the big problem it is made out to be. A fighter that jumps and attacks have to make two checks, one for the jump, one for the attack. A rogue that wants to sneak up has to make a stealth check, then and attack. If you have extra attack, you have to make two rolls (where you could potentially fumble on one of them) As you see every class have the potential to make more than one roll per round. Thats already part of the game. Having spellcasters having to do at least one roll for the success of their spell seems fair to me.
But what you are describing is the equivalent of the fighter needing or make a DEX check to maintain his complicated footwork in combat or a STR check to maintain his grip against the jarring impact in of combat in order to make his attack roll.
A spell is an attack similar to a weapon when the spell requires the attack roll. That attack roll includes abstract variables because it's an abstract system. It doesn't make sense to make an abstract check in order to make an abstract check. This is similar to saving throws in other spells. A d20 is just a simplification of all the variables to determine success or failure to cover it all.
As it is, spells require either an attack roll, a saving throw, both, or the skill check associated with some utility spells just like any other ability. On top of that, there is already an additional roll in the game in the form of the concentration roll if the DM warrants it (revisit those rules), and the option for the DM to simply limit spell casters to wild sorcerers in his or her campaign if that's the style of magic the DM is looking for from the campaign.
DM's shouldn't be over-using rolls on any character regardless of class, regardless.