My estimates were based on comparing EF-S to L lenses, though perhaps I didn't go quite long enough. If I had compared the 55–250 with the 70–300L, I would have gotten a factor of about 2.4. Even with that multiplier, though, it would still be approximately the same weight as a 70–300L. And a big part of the reason the 70–300L weighs as much as it does is because it has a lot more metal than the 55–250. If they made a 24–200 out of plastic, I'd be shocked if it didn't come in under two pounds.
Have you noticed that all the superzooms start at a FF equivalent of ~28mm? I suspect widening to 24mm is a substantial design issue. With a telephoto design, the front element size is the focal length / f-number, but with other lens designs, that's not the case, particularly with wide angle lenses (35mm f/2.8 with 77/82 mm filter sizes). When the 35-350L was updated to the 28-300L, the filter size went from 72mm to 77mm. A 24mm wide end might mean 82mm filters, and a corresponding weight increase from the larger elements.
I also think you're avoiding a logical comparator - the 28-300L's nearest EF-S equivalent is the 18-200. That gives a factor of 2.8. Now, apply that to the EF-S lens most equivalent to the 24-xxx zoom you want, the EF-S 15-85 (L-series optical quality, zoom starting at 24mm). A factor of 2.8 applied to a 20.3 oz (plastic!) lens, and you have an estimate that's a mere 3 oz lighter than the current 28-300L, and still well over 3 lbs. Yes, a 24-200/3.5-5.6 could be plastic and have fewer and smaller elements to make it lighter - but then it wouldn't be an L lens in build or IQ. I think a 24-200L would not be the small/light lens you're thinking about.
We could go back and forth about estimates that very wildly, but the real question isn't whether or not they can make such a lens, it's whether or not they will make such a lens. While mechanical and optical engineering are a part of that decision, marketing is a bigger part. I don't see both a 24-200L and a 28-300L in the lineup, but they widened both ends of the 35-350, so maybe they'd do so again. I think we could see an EF 24-200 non-L as a consumer superzoom, but not until FF bodies come down into the consumer price range (xxD or cheaper). That's the sane reason we haven't seen an EF non-L zoom lens released/updated for over 10 years, with the exception of the 70-300mm (where there's very little benefit to a smaller image circle).