Also remember that id Software wrote an engine specific to the game they were creating (it's debatable whether you can call them engines at all, really). Things are a lot more streamlined if you take this approach because you rarely, if ever, have to answer the question "would this work for some other title?". Or worse, "would this work for any future title that may not even be in the same genre?"!

That, I think, is the mistake many game devs (who write their own engines) make. They make an engine for all possible games, then try to use it for their 2D match-3 puzzler, which uses about 5% of the code they've written, and even then they have to cludge some bits.