Alexander is being disingenuous. He knows that Jonson wrote tenderly of Shakespeare in his Timber Memoir. He's discounting it as evidence without acknowledging it or giving a reason.

" I REMEMBER the players have often mentioned it as an honor to Shakespeare, that in his writing, whatsoever he penned, he never blotted out a line. My answer hath been, “Would he had blotted a thousand,” which they thought a malevolent speech. I had not told posterity this but for their ignorance, who chose that circumstance to commend their friend by wherein he most faulted; and to justify mine own candor, for I loved the man, and do honor his memory on this side idolatry as much as any. He was, indeed, honest, and of an open and free nature; had an excellent fancy, brave notions, and gentle expressions, wherein he flowed with that facility that sometime it was necessary he should be stopped. “Sufflaminandus erat,” 2 as Augustus said of Haterius. His wit was in his own power; would the rule of it had been so too. Many times he fell into those things, could not escape laughter, as when he said in the person of Cæsar, one speaking to him: “Cæsar, thou dost me wrong.” He replied: “Cæsar did never wrong but with just cause; 3 and such like, which were ridiculous. But he redeemed his vices with his virtues. There was ever more in him to be praised than to be pardoned."

Simon Michael Schama, CBE, FRSL (born 13 February 1945), is an English historian specialising in art history, Dutch history, and French history. He is a University Professor of History and Art History at Columbia University, New York.

Good enough as a historian? Schama states that the authorship question demonstrates a catastrophic failure of the imagination on the subject of imagination. Most historians, if not all these days, would agree. There is a prima facie case for Shakespeare, recognised by historians and lawyers alike, which is easily strong enough to disarm dispute.

He did no such thing. This occasioned a reply on Sir Jonathan's Blog.

https://jonathanbate.com/2017/09/22/ted-hughes-marlowe-shakespeare/

Almost everything Alexander has asserted so far is either wrong or misleading.

Sir Andrew Jonathan Bate, CBE, FBA, FRSL (born 26 June 1958), is a British academic, biographer, critic, broadcaster, novelist and scholar. He specialises in Shakespeare, Romanticism and Ecocriticism. He is Professor of English Literature at the University of Oxford, Provost of Worcester College, Oxford, and Honorary Fellow of Creativity at Warwick Business School.[1]

Specimen annotation. Is "cost" the right word here. These are definable complications but not, per se, "costs".