Player health regen starts too quickly, this is a CRITICAL issue imo

This is very important to the flow of basically everything in this game, so please hear me out. Player health starts regening too quickly after you've been shot by default. Here's why this is bad:

• Players don't feel like they're "disadvantaged" if they're damaged but make it behind cover since it regens in no time. There's no stress or change in their decision making because by the time someone pulls up, they'll be full health again. 
• Over time, I believe medics will have their role diminished. Prior titles allowed you to ACTIVELY play a medic role, looking for teammates who were missing health and throwing it to them would regularly score you a "thank you" and points. Here, because health regens so soon, you have a very limited window where you can notice a player is missing HP, close the gap, and throw down your medkit before they're naturally healing already. (If you don't believe me, try playing a single game of BF4 as assault. You'll find dozens of times a game where you can actively heal someone who you notice is low. That doesn't happen in this game.)
• The above issue for medics also makes the training perk from the support class where they become the medkit very underwhelming.
• Infantry regening health very quickly makes vehicles weaker. In prior titles, if you were hit by splash damage/took a few infantry/HMG shots while peeking a tank to shoot an RPG, you had to play super safe, because if you peaked again and were grazed by the HMG/other infantry you'd die because it took time to regen. Here, Engineers can peek again extremely quickly, even if they've been damaged.
• Health regen being so quick means fewer assists, and fewer assist-counts-as-kills. This disproportionately negatively impacts snipers (who have a hard time securing kills if their initial shot doesn't kill) and newer players, since they're naturally less-accurate. Assist-counts-as-kill is a brilliant system, and it's much less common in this game, because players aren't as able to capitalize on weakened enemies, since they barely stay weakened at all.

To be clear, I'm not asking for BF4 level health regen times. That game had like...~16 seconds before you regen health. That's too extreme. But this game has you fully healed like....9 seconds after you're no longer taking fire. Not starting to regen, fully healed. Without a medkit.

If we could instead raise the time before regen starts to something like 8-9 seconds, that creates those intense scenarios where you have to play defensively, makes Support feel better in the long term, helps vehicles a bit, and increases the number of assists players get, which makes the game feel more satisfying. 

And to be clear, I do think that the supply crate will be found to be a lot weaker than people currently think it is. Once more players catch on to how quickly health becomes available, I think that gadget will seem a lot weaker.