Actually, there have been attempts to infer aspects of Shakespeare's character from the plays - for example, quite a common idea is that he was a secret Catholic, based on various Catholic-sounding ideas in the plays.
But it's a risky business. For example, if a novelist writes about dodgy semi-criminal characters (as Joseph Conrad does sometimes), does this mean either he is a dodgy character, or wants to be? Not really.
But this is quite different from HJ, where we have actual documents which describe somebody (Jesus), and historians can argue about whether such a character did exist, or is mythical, or gasp! forged.
If Shakespeare (or in fact any figure in all of human history) was known only from the same
"evidence" that we have for Jesus, then you certainly should conclude that there is in fact no reliable or credible evidence for their existence. To the contrary, you should in fact note that there is quite obvious and undeniable evidence to show why the claimed existence was/is likely to be only untrue fiction.
If Shakespeare (or anyone) was known only from -
1. Unknown writers who had never met Shakespeare.
2. Where those anonymous writers were merely repeating stories from other anonymous people who also had never met Shakespeare.
3. But where those anonymous informants believed there had been still earlier friends and associates who would therefore have known Shakespeare
4. But where no such friend or associate was ever produced or ever known to write confirming any such thing.
5. Where Shakespeare himself never wrote a single word about anything.
5. Where even all the above writing was only known from copyists writing centuries after the anonymous authors and anonymous sources were all thought to have died.
6. Where all the anonymous sources and their anonymous copyists all believed in the existence of Shakespeare as a result of religious beliefs they held in other religious books from many centuries before.
7. Where what they believed about Shakespeare was that he walked on water and raised the dead.
8. Where not a single person in the claimed lifetime of Shakespeare ever mentioned even his existence.
9. Where the one named writer who was not anonymous (“Paul”) claimed to know Shakespeare only because he had seen him in the sky after he was dead.
10. Where that same writer Paul, claimed he knew about Shakespeare entirely as a message from a heavenly God who told him to look in an ancient book of religious beliefs in the supernatural.
11. Where there is not even the tiniest fragment of any archaeological, physical or otherwise identifiable remains of any evidence whatsoever. Albeit, of course there have been numerous attempted fakes of such “evidence”.
… if that was your claimed
“evidence” for the existence of Shakespeare (or any figure at all in all of history), then sensible educated people most certainly should conclude that such
“evidence” is very far short of any standard sufficient to conclude that the person probably existed.