A friend has described Anonymous as an Alternate Universe FanFic, and right good fun if you take it in that spirit.
And here's the thing. Shakespeare's Histories were also set in an alternate universe from our own. He ruthlessly fudged chronology and character when it made a better story. He used biased sources for his background research.
And as Poul Anderson noted and built a novel around, the past of Shakespeare's Histories was more technologically advanced than our own. In Shakespeare, the Rome of Julius Caesar had mechanical clocks and the knights that fought at Shrewsbury in 1403 were armed with pistols as well as swords.
Explicit alternate history can be a very appropriate and effective way to present Shakespeare's histories. Ian McKellen's 1995 Richard III, set in an alternate history 1930s England, is an excellent example of how well this can work.