So this is less about what you do and more about what your opponents do. If your team take shards/wrenches and the opponent doesn’t destroy buildables, you’re more likely to win anyways because you have your buildables up and you have a constant stream of big minions. In capture and faceoff, they are even more valuable because shards are rarer and what you can build is stronger.
There are some good non-white and non-legendaries but they aren’t as universally valuable as the whites, which is my point. I would consider those items tier 2, like a good blue, or a solid purple are good, but not AS valuable as the others. The reason why a 0 cost health regen is better than the others, is because it’s instant and you get the benefit of not having to leave the fight at the very beginning and not have to worry about getting it 2-4 minutes into the game. In that time, you could lose out on a level or two and that would be huge early on. To me, that is worth forgoing to secondary effect for the ability to sustain better.
Edit: @beta382 I responded to a lot of your comments in this.