Consider the front end of a traditional five tube superhet AM radio.
Typical setup is a spiderweb loop or ferrite rod antenna paralleled with a 365 pf variable cap on the same shaft as the variable cap for the local oscillator. A trimmer cap peaks the antenna near the high end of the band and millions of listeners are pleased with the results because all they care about is the local stations. Move up market a bit to a six tube chassis and you gain a tuned RF amp upstream of the detector with a coil peaked near the bottom on the band. The radio tracks better and the sensitivity is fairly flat across the band.
Considering the low cost of chips and the low parts count of a modern receiver there's little to be saved by scrimping on the RF amp... But it's still rare to find one in the typical AM/FM tuner.
Fact is, the limiting factor in the AM band is usually the noise floor. Not the sensitivity of the radio. RF amp or not, few people live far enough out in the sticks to take advantage of a hot receiver that tracks well. Besides, they'll spend more time on the FM side of the dial. If the AM side is good enough to pick up the big signal stations in town it's good enough.
BTW: Do a little web crawling for pre-superhet schematics and you'll find tapped coils along with variable coupling arrangements that do essentially what you're thinking of. A Neutrodyne is pretty much a crystal set with two or three tuned RF stages ahead of the detector and a triode providing some gain with each stage. Tuning involved peaking two or more RF amps and that was done with tapped coils, Goniometers, and variable caps... Which made the superhets extremely desirable by comparison. Two knobs. Tuning and on/off volume. Nothing could be simpler and they had more than enough gain to compensate for any slop in the tracking of the antenna circuit.
Good performance. Easy to use. Art Deco in Bakelite. What's not to like? Ring it up and take it home...