Typically what happens is that folks incorrectly capture parts of both timelines. For "valid time", folks will have "created at", "deleted at", "updated at" fields etc and assume this covers it. Unfortunately, it doesn't really capture proper spans. If I have a fact that starts being true on Tuesday, then add another one that starts being true on Thursday, can I deduce that the first fact was true from Tuesday until Thursday?

No, I can't logically make that claim. It's possible that the first fact was true on Tuesday only, leaving a gap on Wednesday. Without explicit valid time, I can't find those kinds of holes, or apply constraints against them.

Similarly, folks rely on history tables, audit tables etc to try to capture transaction time changes. These are still not enough, for the same reason. You need the span of time, the interval, to properly assert the time during which the database held a record to be true. When we discover that the Thursday fact was wrong, we need to be able to know over what window we held that to be true. Overwriting the record, or entering an update into a log etc, is not enough to truly reconstruct the history. You must be explicit about the span.

The necessity of bitemporalism was easy for me, because I had been responsible for either creating or maintaining multiple databases in which I could not answer a wide range of questions after the march of time. I learned many of the standard hacks (copy the price of a stocked item into the invoice line item, or it will change beneath you! Use slowly changing dimensions! Have a transactions table which creates a slow-as-hell copy of what the database does internally, but not as well!). When I read Snodgrass's book it all went clunk and I've been a wild-haired proselyte ever since.