For one... there's the slippery slope. Each time you lose someone, the loss of combat ability will increase the risk of losing someone else. Thus you start upon a spiral downwards. While it might stop there as it hammers home that you need to work on protecting the party, it might also not. Maybe the heal does not go off in time, or that stun comes just at the wrong moment and bam... you got your second one. And then a third one... and eventually you hit the point where you have to replay a large part of the game because it's now too difficult. Or worse... restart.
Only the most hardcore would ever find that appealing.
If the current system, with its plethora of injury kits, had the system I am suggesting, it would not run the risk of "piling up" on a character until they and experienced a huge number of combat deaths. I would possibly add a kink that injury kits could not be used when there are any nearby enemy groups (hundreds of meters) to prevent a "I got an injury? Let me use my injury kit right now... Dang! Permanent injury. Oh well, time to reload..."
If you make reloading more of a hassle than dealing with the slight injury inconvenience, only the most perfectionist would reload. Or use console commands, for the PC Master Race.
Secondly... a delayed onset makes it less tangible. Even if defeat to eye-injury to blindness sounds logical, it won't feel like it. You won't see the transition happen. It's a pure punishment. A big: "You're not good enough".
The thing is... when games and sport hand out punishment it's to disincentivize certain behaviour. It must come swiftly to connect the behaviour with the punishment and it must be unambigous.
While in this case, the punishment may seem to be: don't let partymembers die. It could also very well be interpreted as a punishment for not taking the toughest partymembers (rather than the ones you want to take), for experimenting with new techniques and abilities (rather than working with what you know works) or just exploring/doing side quests.
And there's always the risk that the brain may never connect a delayed onset punishment with the disencouraged behaviour at all. At which point it's just plain annoying (or game-wrecking).
This is a valid concern. If you disentangle the consequence from the action, it SERIOUSLY runs the risk of not doing anything other than feeling like a random punishment.
But, by the same token, if the consequence is given immediately after the mistake is made, it is far too easy for the player to just reload and avoid that consequence. By sheer luck, even the most passive of players can fall into sheer dumb luck with a fight and get away Scot free. So it encourages the easiest sidestep, instead of encouraging engagement in the game's mechanics.
By that token, I feel the delayed application is the best course of action for this theoretical gameplay element.
Thirdly... We will always seek a way around an obstacle. Often the easiest one. If this is permanent, and randomly applied, that means we have only one way around it: reloading. So this mechanic would essentially add a form of grinding. Do it over and over until success.
The absolute least engaging bit of mmo gameplay... except with load screens... and punishment instead of reward. Sounds appealing, doesn't it?
I would disagree here. Strongly.
Reloading is A) not the only course of action and

not a given for players. You can learn to deal with the consequences and you can learn from them. And if you make reloading the bigger inconvenience of the bunch, then it would be more effective.
After all... we are treating players actually engaging in the combat system as some type of punishment or activity the player doesn't even want to do... that's (hopefully) not the case. The player just needs a nudge to stay awake during the endless string of combat encounters. Not having the same character did multiple times over the course of the game to beat the odds and actually start acquiring enough permanent injuries to REALLY affect gameplay would be... difficult. At that point, it would just be a little nudge to say "hey... There are these things called potions. You can use them during combat!"
Speaking of, tutorials need to exist for a GREAT DEAL of things combat related. While most of the DA systems are logical, they, like so many game systems, are not intuitive by nature. The game needs to TELL players things before it begins assuming they understand them. This can be skill able and optional to see, but it needs to exist. And, if a player begins to fail or do poorly, it needs to prompt the player to consult (or re-consult) these tutorials.
Now the injury system is much weak to do this. Injury-packs are much too cheap. You barely bat an eyelash and it's over. It's not even inconvenient. The tricky bit is of course what would be sufficient? Combat penalties work to a degree, but cannot be too crippling. Backtracking long distances and slowed characters are excruciating and unbearable.
One idea could be that some high end abilities are locked out (or just weaker) on injured characters, big payoff abilities. Things you don't need, but are rather fun and effective. Especially against mooks. Thus, if a character is injured, they cannot use these abilities and thus fights will drag on a little bit longer. Then couple this with injury kits and or equalient spells being a bit less available. Requiring you to do some sort of effort to reap their benefit, but not too much. To add a bit of value to them.
Woah, woah, woah, woah... hold the horses.
You just admonished me for having something that can stack up with one injury, then two, then the whole party until it now becomes impossible to win... but then suggest this?

Locking out abilities is going to make combat harder. A LOT harder. The player is going to VISCERALLY feel that harder difficulty. Unless the skills you lock are not even good ones (in which case, they shouldn't really exist, IMO)... and then, what if the player doesn't have those skills? Would that also result in a player not picking up certain skills because they are one of the "marked for death" skills that get taken out by injury? Oooh... serious problems with this one.
Now, I'm not against injury kits being a little less available. But how would you limit healing spells? They have a set healing cost and a cool down. If a character has it, they can cast it all the live-long-day under the current skill system. And, ultimately, it doesn't solve the problem - the player can have a character fall time and time again, but have zero long-term consequence. Which means there is no reason for the player to change their mindset, approach or even engagement of the game.
And, as I've stated before... when a player isn't engaged, they are bored. You can have pace ninjas doing backflips and fighting with lightsabers and if a player isn't engaged, they will be bored. There is some onus on the combat system, for sure, on that front... but the gameplay design does nothing to encourage that initial level of interest. A new player may freak out when a companion falls in battle, but then sees them hop up after the fight, with full health and mana, and probably thinks "oh, sweet, they can just get right back up." That enforces the idea that letting characters die isn't that big of a deal. If you have that mindset, I argue that not only do you try less, but you also get yourself in more trouble. After all, while one combat death is nothing to worry about, it can make the second, third and (final) fourth one that much easier.
And a player being bored and looking at a Game Over screen more often is definitely a bad thing, I would say.