I've read all the other opinions, and this is mine:
First, I would like to get clarified about the mechanic. So, for example, if a panzer shoots a teammate, the panzer will receive dmg for doing that, but, will the teammate receive dmg?
If the teammate doesn't receive dmg, then I don't like the mechanic. I agree with @Mordecai:
"This may lead to overpowered strats that are only possible in no FF mode, for example you could arty a tank barrier in order for your team to plant the dynamite harmless, and wiping out the other team in the process, with only a minor sacrifice of one person."
The existence of this type of strategies are the reason of me not enjoying no-FF servers as much as I enjoy Hardcore. So, if this is how the mechanic would work, then I wouldn't really support it.
On the other hand, if the teammate does receive dmg, then I also don't like it. I agree with @Aniky:
"Because as u know, not everyone is on the same skill level and gamewise level as certain ppl are. Some players do not understand or simply dont see arty being set or strike being thrown to opponents spawn or strategial position, which will mean that the fop who did everything right will suffer because of that one individual who just plays like a brainless chicken. Second one is that i have experienced couple of times as well and is very annoying that certain teammate will intentionally run into your arties and then complain afterwards, which means u will suffer reflective damage back each time purely because of his dumbness.
It also comes to nades, u would be nading enemy spawn, ur teammate with flamer or something else would run into that spawn, trying to flame opponents and die by your nade even tho he would probably see it before but decided to just ignore it. There are a lot of cases like that, when u check your idea from smiple view, its briliant and would definitely improve a lot in terms of teamkilling or team bleeding, but it would then need to be watched over admins as well, who would need to react quicker than usual if cases like above starts to happen because u can have very fast a big shit storm over situations like that."
So, this would restrict the mechanic to flamethrower, panzer and mortar. The mechanic wouldn't apply to granades/rifle nades, knife, mg42, normal weapons (pistols, smg, rifle, etc.), arty and dynamite/satchel. But it could happen that a mortar is shooting in a good strategical position, and teammates ignore it; then is the same as Aniky said. It could also happen that there are 4 enemies together and 1 ally, and panzer shoots killing the 4 enemies and his ally. That is a good play, even though there was a team kill. The same with flame.
So... I don't really support the mechanic. I prefer to leave things just the way they are now. Just verbal warn, then !warn, then !kick team killers.