A heavy armored fighter should not be able to sneak so easily behind anyone.
Completely agree.
I think the cone of vision debate is also worth having, but honestly, making hide a standard action is really just going to alter gameplay enough as it is, since now the drawback of receiving advantage is to sacrifice one action, which is really the kind of pay-off you should be considering for such a powerful mechanic (not to mention the fact you would now have to position yourself to ensure that the enemies don't see you on their turn. So not only are you sacrificing an action, you're not guaranteed to gain advantage the next turn, maybe the enemy gets lucky and sees you.).
I also think that Hide as a standard action will make Spells like "Invoke Duplicity" extremely valuable in combat situations, whereas right now it's just "meh" (never really understood the usefulness of the "Channel Divinity" slot that Shadowheart has except for this specific spell).