Quite frankly I don't think such a lens design would be sensible. The problem is primarily that you are asking for a zoom. Such constructs always include a certain trade-off in image quality compared to primes. This trade-off becomes more and more visible the faster those lenses are. As a consequence we don't see f1.2 or f1.4 zooms, because it just is not feasible, while f2.8 can be done successfully. A f2 zoom lens could therefore be expected to be reasonably good in IQ only in case it has a rather short zoom range, but then it would not really make sense, because producing a prime in the area of that zoom range would be more sensible. If you look at that article about lens design you will also find that it would be more likely to build a 150-200 f2 lens then a 50-100 f2 zoom lens, because in the latter case the lens design would not be purely telephoto, but a mixed design, because of the lower end being a "normal" length 50mm lens, so it is not a tele.