It is probably more common than you think. But the people doing it have probably never even heard the term "DX". If a station is on the dial, it comes in dependably and regularly, they listen like they would any local signal.
Like any DX, it was probably more common in past decades before the station glut of translators and low power on FM, and the general station glut on AM. A good example was my home town of Midland in the 60's and 70's. The local top-40 station KCRS was censored by the tastes of the Scharbauer family (the S in KCRS, with the C and R the initials of a couple of them. KOMA from Oklahoma City was not censored, and was strong as a local at night. A little fading, but since when is radio - even local, and especially these days HD - dependable? A few of us expanded our horizons further to WLS, which at a thousand miles was showing a bit of weakness for people that had cheap radios. Still, I can't help but think of the multitude of listeners throughout the midwest who were tuned to WLS, KOMA, or on the East Coast WABC. And their lower powered regional counterparts. If you are a kid in a town of 1000 people and the city is 100 miles off, you are a DX'er by necessity, not by choice. And that hold true today, although it is probably more sports enthusiasts or talk show enthusiasts who do the DX'ing for the home team after they move. I still remember the days after Katrina, when NO refugees had portable radios tuned to WWL for hometown news. I would say in refugee centers like the Astrodome - most radio listening at night was DX of WWL. Not that those folks ever hear the term DX, nor would know what a QSL was.
Given the improvement in car radios - just to keep HD marginally coming in reliably - I am sure many people on road trips are DX'ing home town stations without realizing it. Given the 2000 foot towers in Texas, 100kW ERP on FM, and flat terrain you can listen for 150 to 200 miles in some cases. Way outside of the market. DX? You bet and sophisticated equipment.
As far as AM, DX doesn't have to be a flamethrower hundreds of miles away. Getting a 10W low power translator or LPFM 30 miles away qualifies as every bit as demanding. I go in a gas station in some parts of town, there is a middle eastern format from quite a distance, or an Indian one, or Chinese, or Spanish. I don't speak some of those languages, but those people are DX'ing in some cases with haphazard antennas strung high on the ceiling.
And AM - a station 80 miles away just goes ahead and identifies as Houston, advertises Houston, programs Houston. It is actually in Beaumont. And in the Southwest part of town, a 1030 from Corpus Christi booms in like a local. I remember their former format, they were advertising Houston, talking about Houston, acting like a Houston local. And well they should because they peeled paint here. WBAP still programs a lot of information only of use to rural ranchers. You hear them in gas stations as much as 260 miles away (Colorado City rest stop). To those people, it is just a strong station on the dial they enjoy listening to. The very suggestion that they are doing something unusual wouldn't make any difference. They are aware of the city of origin, because of the ID at the top of the hour. But their attitude would be - "don't all stations go this far?"
I often relate my own experience with a new generation of DX'ers. It only took one song from radio Disney, played at a local pool, to get me surrounded by bikini-clad teenagers asking about my radio. Visiting a couple of homes, I found a situation very similar to my own when I was a teenager. An "all American five" tube radio handed down from a grandparent hooked to a long wire antenna, considerably weaker reception than my GE Superadio 3. Somebody else with a really decent portable that was picking up the station. A good knowledge of when KMKI came in best, when an 1160 from San Antonio did better, and when 1690 from Denver came in better. These were self-taught kids, maybe getting advice from parents, friends, the internet - whereever they could get information. I think I spurred the purchase of quite a few GE Superadio 3's in the Lubbock area! Just as kids from the 60's were DX'ing for content, these kids were DX'ing for content.
When it comes to the NFL - adults used to go crazy to DX TV. I have articles on how to build a dedicated pre-amp, for any VHF channel from 2 to 13. Detailed schematic, board layouts, and parts list published by an electronics magazine for football fanatics when the game was blacked out locally. And right there in the article were ads for TV antennas tuned to just one VHF channel, so people could get the game from 100 miles out, 200, even 300 miles out. And that trend continued into the 90's when a friend in Keystone Heights, FL, wanted me to make an antenna for channel 2 Orlando. A quick trip to the hardware store for some 300 Ohm twinlead, and he was set. It was such a good dipole he had trouble with channel 2 Atlanta interfering.
DX is as much about content - denied or embargoed in one location, and people determined to get that content from another location. As long as that type of thought control goes on, DX will go on.