I think they didn't get Henry because he is EXTREMELY busy. He has The Witcher and (around Shazam! filming time) MI6, both of which where he has facial hair. I'm not saying they didn't want another cgi meme surrounding the DCEU, but Henry was probably too busy to go. Plus, it's more secret that way. Plus, they didn't have to pay him a bizarre amount of money. Plus, that cameo probably wasn't in his contract. These are just my assumptions.

My understanding is he didn't want to do the cameo. Which was one of the disputes during his contract negotiations.

Not seeing Superman's head worked. It was funny and a good way to roll the credits.

I had forgotten about it until seeing that scene in the movie, but I thought I had read reports last year that Henry Cavill was going to make a cameo appearance in this movie. I guess I missed this last month, but when trying to search for those news reports, I an article reporting that Zachary Levi had confirmed in a tweet that he had never met Cavill.

@stugood said:

Not seeing Superman's head worked. It was funny and a good way to roll the credits.

I agree. I think seeing Cavill's face at the very end would have given Superman too much attention.

@GForce59 said:

Also, I noticed in the credits they played the John Williams Superman Theme. Was that when Superman made his cameo--the obvious guess--or at another part of the film?

I thought I heard it faintly when Shazam/Billy was flying. Could be wrong.