Mark Andrews had 10 TDs this year and he came out of nowhere, so maybe the talent is not the issue maybe it is a coaching and QB issue.
Maybe Holtz, Horstead or Patterson (Still think he could be a good catching TE) could become the next break out TE with plays that focus on the position.
Counting on Burton, Shaheen or a FA might be a mistake.
I don't know the answer, but Nagy's offense works the best when the TE is one of the primary targets.