The fact that you can frequently hear 1000 watt radio stations on these frequencies is a vivid illustration of why lack of interference is critical on the AM bands, both in the fact that you can hear a station a long way if it has 1000 watts but little interference... and in the fact that that little 1000 watts would be enough to cause easily noticeable interference to another station on the frequency.
The TOTAL amount of nighttime power on 1650 AM is 6,340 watts, split among 7 stations in the US and Canada. By contrast, the total wattage on 1360 at night is about 56,000 watts, spread around about 40 stations, and on 1230 it's over 150,000 watts, spread over about 160 stations. Additional stations at night is one reason that some 5000 watt stations that were huge in the old days now sound like they have really crappy nighttime signals. It explains why you can be in Covington and occasionally hear country music under 1360's syndicated talk shows.
Most of the 1610-1700 band stations run 10,000 days, 1000 nights, with fewer than ten on each frequency, because the original idea was to avoid the mistakes made on the rest of the band. Unfortunately, on those frequencies that's not enough power for decent local coverage, especially at night, although the lack of interference is a big plus. I would be shocked if even five of these stations show up in the ratings anywhere in the U.S.. I see that the station on 1660 in New York has been given 10,000 watts at night, which will help that station but tend to kill off the smaller market stations on the same frequency.
Virtually every move the government's made since the early 60's has been done for the ostensible purpose of making AM more profitable, and virtually every move has resulted in more interference, likely hastening the band's demise.
One idea that would work would be to expand the FM band (using any modulation scheme you prefer) into space abandoned when TV stations drop their analog broadcasts, and put lower power AM's there, leaving only a relative handful of high-powered and regional AM stations, and letting those stations improve their signals. If anyone was able to get this proposal on the table (you can expect special interests, i.e. FM broadcasters who don't want more competition to fight that all way), history makes me fear the the FCC would allow the move, but then renege on clearing out the interfering stations. (This is exactly what happened with the extended band.)
Ironically, though there's no extended band broadcaster anywhere near here, this area is home to the test station for AM digital, which operates daytimes at 1650, behind an office building off Route 4 in Fairfield.