Where did the expression "every last one" come from?

There is, after all, only one last one. Why did it become common to say "every last one"?

Dictionary.com has a definition for last as follows:

8. individual; single: The lecture won't start until every last person is seated.

It seems plain that the definition was created because of the idiom, and not vice versa.

How was the idiom started?

I cannot speak to its origin, but I can speak to the alleged redundancy. There is a reason it works as it does:

Every last one took their seat

The last one took their seat

Everyone took their seat

All three of these sentences mean slightly different things. Referring to only the last one you could be talking about one person. Referring to everyone is too generic and, in usage, it doesn't necessarily mean every single one:

The class will start when everyone is seated

Even after saying such, it is entirely plausible for the class to start before one or two stragglers get seated. By saying every last one, it is clear that every person must be seated.

This also holds for the usage akin to, "The strawberries were tasty; I ate every last one." This implies a much more thorough version of all of them. Plausibly, someone else could have eaten a few or you threw one of the nasty ones away. Using every last one works to reenforce the tastiness of the strawberries and the fact that I singlehandedly ate them all.

There are other phrases that work the same way:

Every single one

Each and every one

These have their own connotations — and avoid the confusion of every last — but they do not fully replace the connotations of every last one. Putting last in the phrase is very powerful.

(The rest of this answer is not terribly important.)

The phrase also has the advantage that it is three short words with a 2-1-1 syllable count. You can verbally morph this structure to emphasize the fact that they are all gone. Every single one is 2-2-1 which is workable, but doesn't quite have the same fast-slow-slow feel to it. More options are good things when it comes to timing and delivery.

This is commonly written by using periods after every word:

I ate every. Last. One.

I personally dislike this style but noticed that advertising from the last decade or two seems fond of it.

The Idiom Dictionary lists this as a variant of "each and every one" which became common from the late 1800s.

every last one; every single one.

Every individual in a group. ..

All of these phrases are generally used for emphasis. The first, although seemingly redundant, has replaced all and every, first recorded in 1502. The first variant dates from the late 1800s, and both it and the second are widely used. Every mother's son (late 1500s) and every man Jack (mid-1800s) are earlier versions that refer only to males.

I can't answer the "Why it became common" though Google Ngrams shows a steady spike from 1880s to 1940s. It seems to be commonly used in writing at that time.

I can find an example from an account in 1817 of Memorial addresses in the House of Representatives

In the expression

Every last one

the meaning of "every" is an anomaly, but only if we deal with pure logic and if we talk about some set whose elements do not change over time or anymore.

Otherwise, in the real world, a following conversation would be perfectly normal (until the idiom; but I hope this can make a case on how idiom could have possibly been constructed):

A: Did you get them all?
B: Yes, that was the last one.
A: What's this then?
B: Wait, let me finish... Done. That was the very last.
A: And this?
B: Oh, no! Sorry. Wait... Done!
A: Hm, sooo, what is it? Did you really get every last one this time?
B: Guaranteed! I checked five times.

So, in real world; or in a world where you analyze logic from a temporal perspective it is permissible to have multiple last, first or otherwise unique members of a set.

In this sense "every" does not mean individual or single, except through the idiom itself, and can¹ be explained with usage of nominal meanings.

¹ Maybe the proper word here is might rather than can. What I mean is that I don't have any references and that the whole illustration is just my speculation.