Elevators are nice. They get you up and down tall buildings quickly with almost no effort. They're accessible and even somewhat social. Yet stairs remain the standard method for traveling from one floor to another. Even buildings with elevators have stairs. Being nice isn't the same as being standard. And being standard is very important.
Stairs are the standard because stairs are reliable. Stairs don't stop working when the building is on fire nor when a power line goes down. And stairs are completely intuitive; you simply walk up when you want to go up; there's no pressing the wrong button.
Beyond practical concerns, a lack of progressive enhancement should raise a huge red flag. While the phrase was coined in 2003, "progressive enhancement" describes how the web has always worked. HTML embodies progressive enhancement; even if you don't have a browser, you can open HTML documents in any text editor and get the content out. At a lower level, the network protocols are built around the assumption that any given packet of data may not reach its destination.
A site built without progressive enhancement should raise questions about all other aspects of the site. Do security precautions on this site similarly ignore all but the most obvious scenarios? Will the site be as incompatible with future technology (e.g. HTML 5) as it is with older technology?
Elevators are nice. But if an architect designed a multi-story building with no stairs, he'd be immediately identified as unprofessional and probably fired. Even if it's an otherwise great building, you just don't leave out the stairs; that would be ridiculous. Some day the web will similarly dismiss websites without progressive enhancement. Even if it's an otherwise great site, you just don't leave basic content or navigation out of the HTML; that would be ridiculous.