Agree, especially in 5E where your primary attribute bonus is so critical to your character. Starting off with a 16 rather than a 12 is the equivalent of two extra Feats after all.If the system is built for it, I don't mind rolling chargen. However, D&D has often not been built for it. Though, I love it in games like Traveller. It is so fun seeing a character come to life in unexpected ways, but ways in which you have a little control over.
This is one of the areas Castles and Crusades shines. Attributes are rolled randomly, but the distribution is B/X, so the primary attribute bonus of a PC will either be +1 or +2; not that big of a difference.
But most importantly, the player gets to choose which attributes he excels at ("Prime"), along with the one assigned by their Class. This offers a whopping + 6 bonus to skill Checks and Saves, making it much more impactful.
That makes you a competent character straight out of the gate, but to further sweeten the deal is being able to add your Level to the checks as well, further minimizing the need for "good rolls".