Can an IGH have the same maximum overdrive-ratio as a crank-sproket setup? Is there an IGH that gives one the maximum overdrive-ratio that one might get with a 39-53T crankset and a 11-34T freewheel? If not, what is the mechanical roadblock in making one ?
If we use the Sheldon Brown Gear Calculator set to metres development (although any other unit will work adequately), we see that the range for a 39-53 x 34-11 system is 2.5 to 10.4 metres developed per crank revolution, yielding an overall range of 416%.

The widest range options from various companies are the Shimano Alfine 11 hub, which has a range of 409% - essentially the same - and the Rolhoff Speedhub 500/14, which has a quoted 526% range.

Compare to a Sturmey-Archer AW three-speed hub, with an overall ratio of 178% based on its stated ratios of 1.33, 1.00 and 0.75.