Did Shakespeare really invent 1700 words?

This was on my list of questions to ask at this site! I don't have an answer but I do have some thoughts and further questions.

Most of these words seem to be variants. If you look at the list here at Words Shakespeare invented, most of these are variations. For example amazement is a variant of amaze. It’s a little more credible to vary an existing word than introduce a completely new one. Also could it be true that there was a lot more improvisation in the language generally at the time due to the lack of a literate populace and established written standards and dictionaries.

First to use in print isn't the same as invent If this was the dawn of English language publishing then presumably Shakespeare was just in the right place at the right time for be the first to print with many English Words.

What of Shakespeare's Rivals? If Shakespeare was in the right place at the right time then so surely were Marlowe and Jonson - I haven't seen similar claims for them.

Does every language have its Shakespeare? I've heard Luther being called the father of German. Would Homer be the same for Ancent Greek? What about other languages?

We don't have a huge amount of writing from ordinary people of the time.

Imagine if the only texts surviving from today were Glen Beck scripts and supreme court judgments we would think that the Fox 'journalist' had created most of the language.