Maybe not party-dependent, but stat dependent for sure. The only other specialization that "requires" a stat is Templar, and that is only if you plan to use the stun/dispell combo a lot.
Assassin and Tempest does not NEED high Crit, but it is a nice addon. None of the mage specialization really NEED a high crit to be effective. Only the Artificer needs it to be effective at anything.
Yes, and no. They all want about 50% crit-ish. Simpy because of the "On crit" passives a rogue get. Not to mention the amount of damage a crit does. It is simply the most optimal way of gearing. Of course, an artificer wants 70%+ to be optimal. Anywyas, at that point an artificer is more than welcome into a team; Even VArric can solo a High Dragon in 12 seconds on nightmare!
To beat a little on the rest of the things you said;
You don't NEED anything to manage. You can do the game, naked, on nightmare and have no problem. Heck, I went 1-15 with 2 level 3 daggers. At that point my sanity was being tested a tad too much, so I had to opt for better gear. So, yes. You are right; You do not need crit to be effective. You also do not need any stat stacking to be effective. You do, however, need it to be optimal. If the goal is to be effective, you might as well go all the way. It cost no more time or effort to get some crit rather than something else.
50% crit takes no effort at all to get on rogues. Mages can reach 30-50% easy as well, given plenty of staves get 25%+ crit (one unique get 25% crit mid-game). Warriors might struggle a bit, but that's okay; 20% or so is enough for 'dem warriors.
The only thing I do agree partly on are assassin. They do not need a lot of crit due to how they work. That said, they still want near 50%. Just so MoD gets a chance to crit, and you get enough stamina back to keep bouncing around in stealth.
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And Artificer gets noticeably better at 30% crit on him/herself, and gets a huge boost once 1, or 2, other team members reach the same.
As my Archer hit 13 (I just got to Skyhold. I literally just got there) I ran to the Forest area. I went in and took out 4 Bears, which were level 16. That got me enough Leather. I used it to craft myself a new set of armor and a bow grip. I ended up with exactly 50% crit. Further or I got the staff at the temple in Western Apporoach. The place where time is frozen. I got the 25% crit staff for Solas.
At this point I could almost spam Long Shot. At level 14. WIth tier 2 gear. Mid-game. Not end-game. Not optimized. My damage was as good as it could be at this point.