It's possible that we will reach a point in computing history where we can run all historical software, and that this state of affairs will continue indefinitely. It just requires enough manpower put into "bootstrapping" of hardware in software (emulation). A decentralized Internet file system might help too.
In other words, the "digital dark age" [1] for code (in addition to documents) doesn't need to last forever.
You might compare it to things like farming, metallurgy, or plumbing. Many things in those areas were invented independently in different geographical areas, and some were altogether forgotten and reinvented later. But now we've reached a point in civilization where we're not going to forget them, because we have libraries, the Internet, and so forth.
Likewise, at some point we should stop forgetting how to run old software as well. Old software can be made runnable now through conscious effort, but the "default" is still for it to rot and be forgotten.
For web pages, the Internet Archive only does the server side... there does need to be an archive of web browsers as well, and there probably will be some day. I have no idea when that will be, but I think it will happen.
[1] https://en.wikipedia.org/wiki/Digital_dark_age