If you still have your old gen console you can play your old games.

First, not if Microsoft and Sony abandon the servers required to keep online-only and multiplayer portions of games running. I already mentioned how the ESA is claiming that nobody but the original publisher has the legal authority to get abandonware servers up as well.

Second, that's only partially correct. As we move further and further ahead, there will be less people who specialise in repair and replacement of old consoles. That ensures their demise, and again, judging by how quickly the industry goes through machines, more and more people will see fixing the old ones as not important and refuse to learn or specialise in the practice.

Lacking backwards compatibility doesn't mean they are destroying history, it simply means that not enough people use the feature to make it cost-effective in new hardware.

These two are not mutually exclusive.

It's far cheaper to produce digital rereleases of popular old games then it is to design a new console with the ability to play all of its predecessors games.

Good point, and if they were doing that, I would have no problem. But publishers are not doing that. The PS2 library, for instance, is arguably one of the strongest console libraries in the history of video games, and Sony mishandled it with such a lack of caring when the PS3 came around that it was borderline insulting. And as I said, all we have to rely on - due to market dominance - in regards to whether or not we'll be able to see those old games again is Sony's good will. Presumably this is the same good will that prompted them to ignore and discard the PS2's entire historical record.