For casters it can be less of thing, because in many cases your stat isn't a big part of what your spells do (in 5E).
I'm not certain this is true, though I would like it to be.
The casting stat is used in three main ways, as I see it:
1. spell-based attack rolls
2. DC on saves
3. number of spells prepared.
1. many casters will have attack spells -- three damage-dealing cantrips require attack rolls, just for starters. Yes, one can choose to avoid these spells, but in doing so you are restricting your character's effective spell list.*
(* by effective, I distinguish that one can make suboptimal choices and one can deliberately impede effectiveness. I'm all about making unusual or suboptimal combinations work, without min/maxing; that does not mean that I want to deliberately hobble a character I play).
2. another area of combat effectiveness can come from spells that require saves (enchantment and illusions spells, for example). Yes, one can choose to avoid these spells too, but in doing so you are restricting your character's effective spell list further.
These two by themselves can be circumvented by choosing specific specialties. The life domain for clerics, and the divination and abjuration schools for wizards, are not especially constrained by a low casting stat based on these two reasons.
Indeed, of the first-level wizard spells (of which there are 11 in 5B):
* four require a save (Burning hands, Charm Person, Silent Image, Thunderwave)
* one benefits from a high Dex (Mage armor, though it does not benefit from a dexterity to a greater degree than not casting the spell)
* three spells are divination (Comprehend Languages, Detect Magic, Identify)
* one spell is Abjuration (Shield)
* two spells are effective in combat and are not penalized because of a low casting stat (Magic Missile, Sleep).
Now while I can think of nothing duller than being a low-level Diviner, there remains over half the first-level spells that are viable. (and divining things will appeal to some players, surely).
3. Your spell casting stat governs the number of spells you can prepare (Stat bonus+class level). This is where you a casting stat really adds to the available choices for the player throughout the entire experience of play. A low casting stat will mean the caster has a meaningfully smaller pool of spells available to her at any given time.
Does this make the importance of the casting stat "less of a thing"? I think you need to work pretty hard to avoid needing a respectable caster stat --
Your effective number of spells to choose from is reduced, your number of available specialties is constrained, and the spells you will have available at any time is limited for the entire experience of playing the character.
I can see this working for a cleric; for a wizard, I think you would need to be a Diviner or an Abjurer, unless you were looking to achieve a very specific experience of play.