You contradict yourself. If replenishing health is the something Halo brought to the industry, then it did set standards.
But setting standards does not have to mean innovating, a game can set standards if it merely popularizes concepts other titles have introduced before. Limiting the amount of weapons you can carry to just two is one of those things, although Rise of the Triad did something similar before (not exactly the same since you could carry multiple weapons, but only one power weapon like a rocket launcher or a flame thrower). Vehicles you can enter and control at will is another (you could drive vehicles in The Terminator: Future Shock, but the vehicles had their own levels and the whole system lacked Halo's flexibility; Codename: Eagle also had vehicles, but its influence would only become apparent with the likes of Halo and Battlefield 1942). Grenades mapped to a separate button is yet another (again, Future Shock did that already; it was ahead of its time in many ways, including mouse aim). Claiming that Halo's success didn't directly influence this industry is ludicrous.
That said, claiming the same for Mario 64 and RE4 is equally as crazy.