English has two be’s, equative and predicative, and both of them seem uniformly to be bad with it-clefts. Compare:
Susan is president / a president / the president.
?? It’s (a/the) president that Susan is.
Susan is horsy.
?? It’s horsy that Susan is.
Susan is under the table.
?? It’s under the table that Susan is.
And for something truly appalling, a wh-phrase:
Susan is who you should ask.
?? It’s who you should ask that Susan is.
This seems to be a fact about the interaction of it-clefts with be, rather than just be by itself though, as many of these sentences are fine with wh-clefts; for instance:
What Susan is is the president.
What Susan is is horsy.
Where Susan is is under the table.
My guess is some clever linguist specializing in the semantics of it-clefts will have to unravel this nice catch of a conundrum.