I'm not going to claim to be an expert on the design of D:OS2, but here are my own observations concerning the points you have mentioned about the combat system in its current state.
1) "Burst damage is too high."
This is true, but it has partly to do with the fact that burst is preferable to sustained due to the nature of the armor system. The quicker you can remove an opponent's armor, the sooner you can chain CC them and essentially remove them from the fight. It's a very binary system and I haven't encountered a situation yet where I would prefer sustained damage over burst in D:OS2.
As for fixes to this... The easiest way to do this would be to have some kind of damage mitigation or retaliation for "tankier" targets. Skills that reflect damage (like the pain reflection attribute, but as an active you plan around rather than a passive that doesn't encourage decision making), or skills that cap/prevent damage from passing a certain threshold could work (Protective Spirit from Guild Wars: single instances of damage cannot do more than 10% of the target's max hp, excluding conditions). I'd even be in favor of a talent or skill that absorbs all excess damage/CC when your armor drops to 0, similar to how Comeback kid prevents death upon HP dropping to 0. It would synergize well with the existing shield skill. It would have to be properly restricted/balanced in order to prevent it from being something every character dipped into, though.
2) "CC is too effective."
I absolutely agree; any fight can be closed out when you remove an opponent's armor since they are then vulnerable to being chain CC'd until they die. This is a widely talked about problem on these forums but there's never really been a proper solution.
The abundance of hard CC that have no behavioral differences is what I would choose to blame here; there's little to no mechanical distinction between knockdown, stun, frozen, and petrify. There are a lot of skills that can cause these statuses and any one character is likely to have at least three of these available to them in their standard skill loadout. I'd like to see more importance placed upon softer forms of CC that are more situational (Cripple, Blind, Curse, and even elemental statuses like chilled, wet, warm, etc). In D:OS1 elemental statuses had a much bigger impact on gameplay and I kind of miss that. These elemental statuses were also versatile in their ability to protect yourself against certain forms of CC (VS ice, you could warm yourself to prevent being frozen, etc), while also being able to weaken foes to your own statuses. Softer CCs and statuses like these that don't lock out action encourage problem solving from the player, and could be a possible solution to the currently binary nature of the armor system. It was also nice to be able to remove CC with utility skills (Haste removing frozen by applying warm, maybe earth could "ground" shocked characters somehow?), the elemental interactions eased the rigidity of there being an abundance of hard CC by supplying a variety of solutions to the player beyond "have frost armor or fortify".
To be clear, I don't think all forms of hard CC should be removed. It's just that in the game's current state there is way too much of it and it's not uncommon for fights to quickly turn into something where hard CC is king.
3) "Hybrid teams are discouraged."
I feel like this is a larger problem for magic damage than it is for physical: usually physical damage dealers will have a tiny bit of magic damage from their elemental weapon bonuses (which is a bit counter-intuitive).
I understand what you mean about the "two separate minigames" comment, though. Usually with a bit of preparation I've always had access to the kind of damage I've required though, be it through dipping into different schools or by using consumables like arrows, grenades, or scrolls.
However, my most successful character was a staff-wielding mage who dipped into fire and warfare schools. She was able to target both armor types somewhat effectively and play off of the damage types of the rest of the party.
4) "Positioning means very little."
Most of the positional play I found effective was to abuse AI and funnel enemies through choke-points on the map; it felt more cheesy than tactical. I don't think having movement abilities share the same cooldown would fix the problem, it would just feel like an arbitrary rule specifically meant to target the problem, rather than a proper solution.
My suggestion would be to improve the importance of soft CC and controlling abilities. Blind can already prevent movement abilities because it limits the LOS required to use them. Cripple could also be buffed to prevent the use of movement abilities, and could be a possibility for an offensive form of how "Fortified" prevents forced teleportation on allies. Movement crippling effects like Slow and Chilled could also proportionally reduce the distance these skills can be used, but I'm not sure if casting range on specific skills can be applied to scale with movement speed.
This essentially has to do with the ineffectiveness of a "tank" character. There should be ways to lockdown an enemy beyond bursting through armor values and chaining hard CC. I've seen people suggest adding a "Taunt" to the game, but Taunt would only just be another form of hard CC which we have way too much of currently. I'd like to see tanks impose their presence through existing controlling effects like cripple, Attacks of Opportunity, blinds, and more dynamic methods. Larian originally wanted to include push/pull effects which would have been great for this, but they weren't able to due to the limitations of the engine. Additionally, your suggestion of having ways for a tank to protect party members through damage mitigation (or even CC mitigation?) is something that would work as well.
For an outside reference, D&D4E had a sort of "soft taunt" system that would place heavy penalties upon enemies for ignoring a tank/protector. I'd prefer something like this to a hard taunt that just overwrites the AI to attack a target mindlessly.
Apologies for the wall of text, but I hope it was constructive, at the very least!