Oh, I agree. Nice sweet & sour punch. But, in my experience, beets in general are just not a favored food in the US. I mean, they’ve gotten much more popular over the past few years, but I think they are still regarded with suspicion by a lot of folks. At least that’s how it seems to me.
I’m the only American I know who actually likes beets. But as a regular vegetable in their own right, bought fresh, greens and all, and made into borsht. I’m not acquainted with them being pickled, except in a Persian *torshi *blend, where they’re used in moderate amounts to turn the turnips or cauliflowers pink, or likewise used to turn Pennsylvania Dutch pickled eggs an intense pink.
What is that stuff in the jar? It looks like yellow relish.
I like beets too. Pickled is best but little ones with butter are also good. Do not like Harvard Beets, however. Never thought of putting them on a burger but it sounds good.
You know, this thread just cries out to me that someone should try the empirical approach. That being said, I think I prefer the lettuce on top. I hate when the bottom bun starts sliding around on the patty.
I didn’t vote because I have no preference, except for a burger with two patties. Then, I want “salad”/fixings on the top and bottom because I eat the burger as two open-faced sandwiches. Ate a burger that way just last night. And yes, it had fixings on top and bottom without me asking, so I must not be the only one. 
So your not from around here. That would explain it. I don’t mean to sound chauvinistic or anything but putting beets on a hamburger just sounds . . . . un-American. And I’ve never heard of hamburger fixings called “salad” before.
if you put the salad below the meat then the burger will slide right off.
So from the perspective of us northern hemisphere folks; the Aussies and Kiwis actually put their salad on the bottom. -----Just kidding, the old upside down joke.
Start with a less than gigantic bun, toasted lightly to increase the surface tension(?), I put a slice of raw red onion on. Just a few of the rings - the onions can get overpowering. Then the patty; not some massive thick blob; thinner, coarse ground, not hard packed - closer to loose. Then some 'shrooms. Finally a good cheese, again not too thick followed by the top bun. I’ll be having my lettuce/greens/tomatoes in my salad, thank you very much!
Depends where “here” is, but I was born and raised in the US.