You do realize this entirely writes off any history not backed by archeology, right? I mean, I'm not going to say there aren't problems with history, but that seems an extreme position.
History is not a statistical science. It is our best attempt at assembling
some idea of what happened in the past. That idea is
often wrong, and any good historian will tell you that if you base your stuff only on secondhand information, it's
bad history. Further, any good historian will tell you that even with extensive primary sources, we can still be led astray if all of those sources are biased for the same reason.
Finally, while the ravages of time do act as a selection process, that selection process is not nearly as biased as
people volunteering information by self-selection. It IS biased, but the bias is (usually) much more random, which means the data we derive from it can be more meaningful, even if not absolutely so.
Archaeology helps us do
the best history. In the total absence of physical data, we rely on a diversity of sources and recognize that sources, even primary ones, are
deeply flawed.
Consider ancient Norse religion. It is
almost certain that we don't actually understand what their beliefs were, because for whatever (IMO ridiculous) reason, they chose to
never write down their religious beliefs, using
only pictorial depictions (e.g. carvings of scenes on megalithic works) and oral tradition. It was only when Snorri Sturluson wrote down the
Prose Edda, long after Christianity had completely subsumed the Nordic territories, that we got anything, and he is
notoriously biased because he wrote that work specifically as a political tract to persuade Iceland to unite under other Scandinavian royalty. Not to mention that the work is so thoroughly Christianized, it tries to pass off the Norse gods as
completely mortal heroes of ancient Troy!
We do what we can with what we have, but we do so knowing that it's almost surely got parts that are wrong and we won't know which are which. So we make damned sure our conclusions are small and conservative.