> I want AM
WHY???
I'm not just being wise-ass. In most civilized areas, AM radio means major compromises. What you want AM for determines what the radio must do.
As sad as they are, the general run of $2 AM radios do about as good a job as is possible. You need some special situation to do better.
If you are "close" to a strong station, a wide-band AM tuner can reveal a spectacularly faithful reproduction of what they put in the transmitter. Much more treble than you expect. Can't avoid the fact that most AM today is grossly over-compressed. That's the only way they can keep their business going.
If you are far out in the desert, and want to pull Denver or L.A., you want a decent antenna, ample gain, and lots of selectivity, to the point that you don't hear anything over 3KHz.
If you are near town, and "your" station is not very much stronger than others, about the best you can do is a little gain and a LOT of filtering to knock the crap down. Any non-junk $2 radio will do that. (Yes, there's some real junk on the market.)
I spent several years tweaking on a golden-age Stromberg-Carlson.
In my suburban area, antenna and gain were non-issues: a loopstick or 2 feet of wire pulls-up more noise than you know what to do with.
Wide-band opens up the treble, but also opens up monkey-chatter from every adjacent-channel station in the US and Canada (and Mexico too, if the Canadians weren't overwhelming Mexico in my area).
And you can't avoid the fact that AM does not lock to a signal(*), so you get every same-channel station underneath the one you want. (There are no "clear channel" allocations any more: one former clear-channel broadcaster in NYC now has 17 other western hemisphere stations on the same channel, from 25 watts to 25KW.)
(*)Actually, a synchronous detector can give some AM lock-in. My father the old-time radio geek didn't believe it at first, because sync-det was just way-difficult back when AM was king. It is still a very difficult problem. The only practical answer is a chip. Maybe someone has done that. I notice that none of the marketed radio chips do anything fancier than ceramic filters and a buffered detector.
> Is it possible to build a "higher quality" AM band receiver, than I can buy?
If you have a Strong Local Station, a crystal radio will give great results, and is certainly a DIY thing. Understand that most listeners don't want quality, so the broadcaster hammers-up the sound to stop them in their tracks. You'll mostly hear how modern broadcast limiters can slam everything into a 3dB dynamic range without getting fuzzy.
A TRF with a large (10 foot) loop can give sharp sound a bit further out, but parts for a TRF are hard to source. If there is ONE station you want, it is maybe doable. But tuning a 3:1 band is hard work even if you can find the gang-caps.
People DIYed superhets, but it seems to be a lost art. And certainly you can't get the parts without scavenging a radio, you can't get the good parts without scrapping a good radio, and it is surely easier to fix the radio than re-engineer it.
I've heard the GE and Tivoli are good. These and the Golden Oldies are surely better bets for all-round AM use than any DIY except a crystal set.
(In Los Angeles) sensitivity and antenna are nearly non-issues. Aside from the universal earth-made static, cities are full of man-made noise, and also chock-a-block with AM signals. And even in sprawling LA, you can't get very far from a transmitter, or at least you have a choice of nearly equivalent programs from near and very-near towers. A foot of wet macaroni will pull enough atmospheric noise (and signal) to overwhelm the worst input stage's self-noise.
PRR