Ideally enemy oneshotting would also be minimal. Enemies would deal enough damage that getting caught in a bad position would feel dangerous, but not so much that players wouldn't be able to manoeuvre their way to safety if they reacted quick enough. I've recently started playing Vanquish again with the aim of staying in cover as little as possible (instead using evasion and boosting to get out of the way of enemy fire), and I'd say that general level of difficulty would be a good balance for Warframe.
While the relative number of enemies in Vanquish is generally lower, a similar effect could be achieved by restricting how many enemies can attack a player at a given moment (IIRC, DOOM 2016 actually uses a system like this, so it is possible). This would preserve the feeling of tearing through hordes of enemies, but allow DE to tune enemy damage output around smaller numbers. Such a system could also be scaled to make a difficulty curve. The stronger your gear is, the more enemies can attack you at once.
A mechanic that I was considering suggesting would be the addition of something akin to SAO Fatal Bullet's prediction lines to hitscan attacks. That way you get a split second of warning before the damage hits that allows you to react (Projectile and melee attacks wouldn't need this, as they are inherently telegraphed). No more out of nowhere health loss.
Forgive my little ramble, this was a bit of a stream of consciousness.