Die Hard itself wasn't intended to be a
Die Hard movie. It is adapted from the novel
Nothing Lasts Forever by Roderick Thorp, a sequel to his novel
The Detective which was adapted into a film of the same name in 1968 starring Frank Sinatra as flawed NYC cop Joe Leland (incidentally also the film project that essentially broke up the marriage of Mia Farrow and Sinatra when she chose to do
Rosemary's Baby instead of co-starring with Frank in his film).
Nothing Lasts Forever was originally envisioned as a movie starring Sinatra reprising the role, but he passed on the project. It bounced around for almost ten years before TV star Bruce Willis was attached, the references to
The Detective all removed.
Plenty of details had to be changed from the novel, crucially making the protagonist much younger, changing the character of his daughter who worked at the company under siege into his estranged wife, and making the ultimate goal of the terrorists a theft, but the spine of the story is very much the same and many of the iconic set pieces were taken directly from the book.
And to answer the original question, no,
Die Hard is not at all overrated.