His plays really do have something for everyone. They appeal to everyone because they have a little drama, romance, comedy and action all in one play. There are also a lot of different kinds of plays, so different people can choose their favorite.
I think this idea is oversimplified. Shakespeare's audience was quite middlebrow--no lower classes, but also not upper classes (except, perhaps, Midsummer Night's Dream, Twelfth Knight, etc. which seem to be written to be presented for wealthy families in their homes. There were plenty of opportunities for entertainment for the people you descrcribe--bear-baiting, for examplem not to mention the boy's companies which are excoriatedin the Folio edition of Hamlet (the "little eyeasses" in II.ii).
Don't believe everything you hear.
Shakespeare did not write plays that could necessarily be easily categorized in one particular genre. For example, Romeo and Juliet is not just a tragedy or a romance; it also contains elements of action, comedy, suspense, and even horror (the crypt scene). Shakespeare was incredibly talented at creating characters and situations that appealed to a broad range of people. If an audience member did not care for the idea of a love story, then perhaps the fighting and murders would intrigue him.
It is also important to note the Shakespeare did not maintain the same mood all the way through a play. He was sure to include humor frequently in his writing; sometimes, the humor is understated, sometimes it is outright.
Shakespeare, like all great authors, knew his audience. At this time in history, men were largely barbaric, violence-and-sex seeking theater-goers. In some ways, it wasn't all that different from today.
To satisfy the men in the audience, Shakespeare always included conflicts that went beyond emotional and mental realms and into the physical. So, those seeking "action movie" type culture were kept content.
For his female patrons and those who were more sensitive, Shakespeare mastered romance in all its intricacies. Whether it was the flames of passion between Romeo and Juliet, or the twisted and complex family lives of his other characters, William Shakespeare knew how to intrigue his diverse audience.
I think that shakespeare entertains his audiance really well. he puts in lots of violence like at the start of romeo and jeliet both families are fighting and theat gets the audiance going because the groundling who wantch the plays have a lot of violence in there life's.
That is why his plays work on so many different levels. Even if you couldn't read or write, you saw a lot of violence and death and that would be considered exciting. To the other end of the spectrum for people what were well privilegedand understood nuances of language, you could find that in his plays also. It seems that there was something for everyone in his plays so that no matter what station in life you were, you would find something worthwhile. And who doesn't love a good ghost story now and then.