Is it technically even possible to reduce the input lag to tolerable levels with the old chipset?
It can, unless the chipset is already maxed out of it's capabilities. I know Panasonic and LG have patched in features for years. Some devices had HDR10 patched in, but given they support DV already, it's not that hard.
LG has promised to patch their OLEDS to improve 4K HDR game mode imput lag, and that was only after there was a dedicate campaign to get it fixed. I have a feeling that Sony either doesn't want to invest engineering time to improve it, or they can't. Either way, trying to suppress the truth and being silent in PR was not the way to deal with it, especially if this blows up and it leaves the gaming community.
If it doesn't Sony will probably sell well this holiday anyway, I know many people who think "Sony Bravia, PS4 Pro, that can't go wrong, right?"