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If there is no threat mechanic, then tanking is a lot more abstract in my opinion. I prefer threat mechanics. Not just as an occasional tank, but as any role. Particularly dynamic threat mechanics like tp that let the enemy react differently depending on how much damage is done to them at once that lets them do special abilities through out the fight like in FFXI. If hate isn't dynamic the game is too simple for my taste and tanking becomes very bland. You don't need fancy ai, just dynamic threat. We have a really old game that worked very well to prove it.
I feel like I have a unique perspective, as I enjoy tanking in some games but not others. I don't like games where they make it impossible for me to tank in the scenarios that interest me in tanking as I tend to play classes that can easily spec into tanking. When I do tank I tend to prefer to either off tank (ie hold focus on a secondary add for part of the duration of the fight OR swap tank with with my primary tank for part of the duration) OR tank for specific types of enemies that are more about positioning, quickly adapting to an enemy, and mitigating certain types of adds. Usually these fights tend to be against spell casters, dragons, or really anything that does magic as main damage and requires a lot of spacing from the party.
When I tank, I do not prefer to hold threat personally, I rather do it from a separate entity ie a summon. The reason I like tanking as a summoner is when the enemy is mainly magical in nature and requires a lot of mobility from the rest of the party. I prefer tanking such targets over my paladin because it frees them up to off tank more physical based adds, and frees up the party to focus on spacing. Usually I'm primary tank for these types of battles but need a secondary or off tank to help me mitigate adds or help me swap summons to switch to the right elemental resistance.
Additionally summoners in another game I play are good at having their loyal summon tank. So when an enemy uses Charm I can continue tanking because my summon does not get charmed, even though my team can get charmed, and I am able to run away from the range of the charm in time. I usually am main tank for these types of battles.
I love mitigation style abilities where I can swap threat between me and my summon. I love mitigation in terms of damage reduction, summoning temp hp buffering shields, and other forms of damage reduction. I love supporting my team with these as they lead to far more interesting and dynamic fights.
To answer your key questions:
Yes it should be part of combat initiation. Yes it should be throughout the entire duration of combat. Yes you can make threat pulling moves for tanks and hopefully as an augment. To make it work in PvP just make it force the targets reticle to focus on the activating player.