Things were being done with computers before the first httpd was run. A great deal of them were very clever. Most of them are still relevant today, if you know of them, if you know enough of their background to appreciate them, and if you know enough of the fields they came from to understand them.
When I was a wee lad, "everybody" was mucking around with home computers. 16 bit machines were just around the corner. They were going to crush the minicomputers; VMS was slowly but steadily extinguishing UNIX. Oh, and the future of professional programming was in Ada.
Who knows? You might find something else you like doing. Or you might decide that the Web really is the best. But at least you'll know enough to bring new ideas to your field. You'll have an easier time seeing others' new ideas in their context (and seeing if they're really new!).
Knowledge is Power (no, really).