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Why do lingering stat maluses exist?

I think they represent you still being in huge amounts of pain/sore, even if your wounds have been patched out.
That's how I play them. And to be honest, I've yet to have them really ruin my day. A minor inconvenience at most. I just try and keep them in mind as I go about. Like remembering you have a sprained ankle.
I don't mind the maluses and think they could even be made more common or severe. This encourages fun stuff like beating the hell out of a guy before his UMC bout 'cause you bet on his opponent. I've only noticed them when getting hit with really powerful weapons.

Maybe taking a bunch of painkillers/having a Pain Editor should clear them entirely so you have a way of getting back into the fight quick. But you can already use drugs to boost your stats back up anyway.

I think the point is… to represent critical damage and realism in taking a severe physical punishment?

I've never had to explain that before... >.>

As far as I know, yes, your stat damage largely heals at a different rate than your health damage and can persist even after being brought back to full health. It's intentional as it kind of represents taking very hard hits.
These penalties exist precisely for the reason you mentioned. Healing is cheap and easy and with the addition of a healing stim patch you can be back at 100% health 15-30 minutes after a fight if you are smart about it. However your character just went through a serious trauma and there would be longer term repercussions that would persist for taking critical damage. This is a common enough thing in most gaming systems, be they table top or video games.

I think a more productive direction for this conversation to go would be:

How can we better represent, both to the character with the stat penalty (I don't know what malususes means nor can I spell it) and to the characters who see that character, that they are still in pain despite their wounds having been healed and bones mended?

Send players a message about being in pain whenever they make a skill or stat check using a stat that is lowered from damage? And maybe add a more robust system in general for players to assess their own or the wounds of others IE: limping, getting 'stunned' like you do from certain situations when you're exerting yourself while heavily injured (mitigated by cyberware?), dropping things you're holding or being forced to sit and be unable to stand for several moments, etc
Stat rolls happen too often to send a message like that every time. There is already an indicator in @stats that a stat has been effected. Perhaps a status message in @stats? Perhaps a modifier to the health message so it's like…

'in excellent condition but still recovering from previous injuries'?

I think a modifier to the health message would be enough, and the way it would be the most clear. I've had my mind on this for a while now, myself, and I think while the system is fine – It's just not clear enough.
I have always tried to model this on my own to be honest. In general, I try and set my @lp in cases where I have stat damage or covered wounds but am otherwise healed. I mean, it has always been clear to me when I have lingering damage beyond health just by looking at @stats and @nakeds. It's just advertising this to the outside world that needs help in my opinion.

If my health message is anything below excellent, I don't worry about it too much. If It is excellent or better and I still have wounds (like bruises or cuts on @nakeds) that are unexposed or stat damage, I add an @lp to help describe my state to the outside world. Typically, this is straight forward. If my leg is bruised my @lp is 'limping slightly.' If my arm is cut my @lp might be "is favoring their left arm". If my abdomen/chest/back has a bullet hole my @lp is "wincing with every move." And so on.

I generally keep this message in place until both stat damage and the wound are gone. The problem is that I don't always remember to do this and I sometimes forget to take it off. I'm not saying that this is the best solution but I thought I'd share it in case it sparked ideas on an automated solution.