Some type of panel or electrostatic speaker. Magnepan, Sanders, MartinLogan, etc. I've read that Magnepan won't even submit their's for test as they don't get good results. Yet lots of people like them (myself included). It would be interesting to see the data and resulting discussion.
I think most of that has to do with Stereophile's measurement methods. There are several issues.
One is that they they measure bass response in the near field. You can't do that with a large dipole, as it will show a large apparent bass boost. They have to be measured at a typical listening distance so that dipole cancellation can occur.
Another is that it's challenging to get a meaningful waterfall plot from a tall line source. The speaker has to be far enough from surfaces so that you can gate our the room reflections while still getting a meaningful measurement. Which pretty much means you have to fly them outside or in a gymnasium. (If you measure them up close in a normal room, you'll see a very clean waterfall, but it's questionable what *that* means as well.)
Then there's the matter of room interaction. This is an issue with all speakers, of course, but as anyone who has ever set up dipoles knows, it's more of an issue with dipoles! There are both positives and negatives here. Among the negatives, front wall reflections produce a dip in the range from 100-200 Hz. Omnis have a similar issue (at different frequencies), but with an omni, you can split the difference between the x, y, and z axes to minimize the effect, whereas a dipole gives you little leeway and results in a dip that can't be equalized out. The other is that dipoles don't excite the x- and y-axis axial modes. This means that they have a smoother bass response in an ordinary room than omnis; in practice, you need to use four omnidirectional woofers to get comparable response.
Finally, I've been told that JA aligns his measurement microphone with the physical axis. That likely works with a loudspeaker in which the drivers are arrayed vertically, but when they are horizontal, the crossover lobes will be horizontal and the maximally flat response will depend on the specific crossover. Which is to say that the proper listening/measurement position for determining on-axis response will depend on the crossover.
Another consideration -- the 1 meter sensitivity spec of a line source is misleading since the radiation of a line source falls off as 1/R rather than as 1/R^2. So at a typical listening distance the effective sensitivity is higher than the 1 meter measurement would suggest.
Finally, there are some things that aren't reflected in the typical measurements at all. One is that the dipole radiation pattern has specific psychoacoustic effects. An omni/cardioid will reflect mostly from the side walls above bass frequencies, and this will tend to broaden the image. With a dipole, on the other hand, the side wall first reflections tend to be weak because they fall in the dipole null, while the front wall first reflection and the front wall second reflections are strong. In practice, this means that they will develop enhanced depth rather than width, particularly when they're far enough out from the wall to delay the first reflection by 20 ms or so (a good concert hall has an ITDG of 20-25 ms).
JA has a good discussion of some of these issues in his LRS review:
https://www.stereophile.com/content/magnepan-lrs-loudspeaker-measurements
But many people skip the text and just look at the measurements, and that's why Magnepan has an issue from a marketing perspective. If you look at the measurements of the LRS with these caveats, you'll see that what the listener actually hears is good on-axis response with a gentle house curve, but if you just look at the frequency response without taking these considerations into account it looks dreadful -- absurdly emphasized low end, suckout at the crossover point, and tilted down.