There are about 15 champions without mana or energy. And some of them still have resources they rely on. Fury, Rage, and Courage just to name a few.
There are very few champions that have no resource other than health. Garen, Kat, Riven, Zac , Yasuo, Vladimir and maybe Morde.
There are more than 130 champions in game at present.
That means less than 12% of all champions have neither mana nor energy and less than 5% who have no secondary resource at all.
So we can safely estimate that 8 or 9 champions out of every 10 champions in game overall have neither mana nor energy.
Given the trend of recent releases. The amount of champions that have neither mana nor energy is an estimated 1 out of every 5.
You stating that no resource champions is better than 90% of the rest of the pool is like saying, "no resource champions are better than the 110+ champions that are available for purchase and play".
Ability spam? There's a thing called cooldown and no matter how much CDR you build, you will always have cooldown. If a Riven or a Kat or a Yas decides to spam their entire combo then you can bet I'm going to jump on them before they've a chance to say "No, I don't like anal".
Mana is not that crippling. It's called resource management. You use what you need to get what you need. If you're spending all of laning and early game wasting mana on creeps then you deserve whatever the enemy has to dish out. But if you can manage your mana wisely then come mid to late game, it won't be as much of a handicap.