The bottom line is that the channels make more money airing the ads (Billy Mays, et al.) then if they aired programming and sold ads. This is because the ratings are so low overnight, and because the As Seen on TV 30 minute ads DO WORK, and, so the Billy Mays folks are happy to pay for the block of time.
The really sad part is that these 30 minute informercials paid programming are now being aired during the waking hours of say 7AM-6PM. Yup, these commercials are so successful that now they are willing to pay the higher rates during the waking hours, and, yes, the stations air them because they make more $$$ than if they were to buy the rights to programming and sell the air time for 30 second ads.
Those of us on the west coast get the paid programming at the still waking hours of midnight on the sat channels. However, those on the east coast have to endure the paid crap as late as 9AM, while we here on the west get the reprieve as early as 6AM.
The only channels that still air programming during the wee hours instead of paid crapola are channels that get such low ratings overnight that even Billy Mays won't pay to reach the 5 or 6 people watching that channel. Such channels currently include Science Channel which is in the highest tiers of almost all cable and sat as is BBC America because they too came late to the game and are only in cable digital tiers and at the higher tiers.
This means the very nanosecond those and other channels start to get a few more people viewing in the wee hours, they WILL sell the time to As seen on TV. History International was paid programming free for years, then they got more viewers and now it is Billy Mays overnight. UUGGH. I share your grief.
Your best bet is the highest tiered channels for the hope of real programming overnight. This includes just about all the channels offered in HD with no SD equivalent channels. Yes, I have watched whatever is on HDNET, and even very recently LOGO, although a joke as HD, but at least they have some crazy stuff to watch overnight.