There's one catch, though: modern TVs lack an input filter that they're supposed to have by design which would normally reject non-TV frequencies,
If they are lacking the filter, then they were designed that way. Those devices are FCC approved and certificated, and if they were designed and tested for compliance with the filter but are being built without it, they are in violation of federal law (47CFR15) and can be confiscated and destroyed.
Designed and tested with the filter, shipped without it because they're expected to be connected to Cable, AFAIK. As for confiscation/destruction, I don't think that's realistic, regardless of whether that's what's "on paper".
In those cases filtering needs to be added back to the TV to isolate it from the Ham transmissions -- it's my understandnig that this filter can be provided by the TV manufacturer upon request.
Since it is not really part of the design, and the manual for the TV clearly states that this device must accept interference (as part of the Part 15 Class B conformance statement), probably not. I think you can find commercial filters to use in this case, but the TV owner is stuck paying for them. And good operating practice says that the ham is not going to touch the TV to try to fix it, otherwise he becomes liable for any perceived failures of that TV. "Hey, the day after you installed your filter to stop your interference, the TV stopped working altogether, and I'm suing you, you basterd."
And, sadly, most of the interference issues would not be solved by installing a filter on the antenna,
That wouldn't help at all because the issue is the TV being desensitized by a signal that is out-of-band for TV, but in-band for Ham radio. You cannot filter out the signal that you're trying to transmit, as that defeats the purpose.
since a lot of the interference issues comes from modern, cheap ass plastic housings on the low price consumer equipment. You can't stop an interfering signal that is leaking into the electronics through the side of the TV by installing a filter on the antenna lead. You need to install shielding on the TV itself.
Well, no, not in this case -- remember, we're talking about TVs receiving broadcast TV that are the problem -- the signal causing the TV a problem is coming from the TV antenna, and (generally) not from "leakage". You've got the right idea, though -- that the receiver needs to be isolated from the desensitizing signal. Some filtering between the TV antenna and the TV is all that's required to reduce the mount of the Ham transmission gets to the TV's receiver. The TV's receiver is in a separate RF enclosure, so the fact that the back of the TV is plastic isn't a problem and is thus (usually) a Red Herring here.