I love that there is aggression by animals in the game and it does raise the tension a bit, but honestly I have never felt a serious rush where I really thought I'd lose. The animals just don't do enough damage when they strike and require multiple (like maybe 8-10 hits) before you'd actually "die" from the encounter [if at full health]. The need for med kits isn't really that critical because of this. I think an increase in animal damage would add a new element to gameplay. Maybe have damage based on animal type/size (like a cape buffalo charge would do more damage than a fleeing roe deer running past you) or strike method (gator bite hurting more that a wolf bite). I think this would make encounters more exciting in order to fight for survival.
And tying into this would be predator hunting. Right now they do spook animals in the area when they come close, but maybe have them actually succeed with a kill. It'd be cool to see a lion take down a gemsbok for example. To make it so that it wouldn't cause players grief in getting trophies, limit kills to the lower level animals like 1 or 2 (bronze and silver) to simulate them picking off the sick, weak, and slow animals. This way gold, diamond, and great ones aren't affected. This would allow for respawning of animals usually ignored and would add a dynamic in managing herds (sort of like Way of the Hunter), and change up the unpredictability on getting rare fur variations, etc. It has the potential to increase the surprise/wow factor of the game.
Just a few thoughts on potential game improvements.