The analogy to running is throwing the discussion off-track, because you can only run one distance at a time. Or to put it another way, running has two dimensions (time and distance) while lifting has just one (weight). When someone runs ten miles twice and then says they've run a total of 20 miles, we implicitly understand that it took them twice as long as running ten miles once, not that they doubled their speed.
That said, the relevant question is whether tracking cumulative weight lifted is misleading, or has any implicit meaning. I'd argue its meaning is clear. Consider Tennessee Ernie Ford's 1955 chart-topper, Sixteen Tons: "You load 16 tons, what do you get? Another day older and deeper in debt." He doesn't mean that he lifted sixteen tons of coal all at once; that's the cumulative amount he loaded during one full day. It's a meaningful metric to him, because loading 16 tons is harder than loading 15 tons, and easier than loading 17 tons. Similarly, his total loading numbers over the course of a week or a month or a year tell us something about how hard he worked, and perhaps how much he earned. So the idea of adding up a bunch of small lifts to get a single number analogous to a big lift has a long and established history that dates back to well before social media.
In summary, chill out and worry about your own problems, dude.