I suspect that many problems, especially in the big cities, are due to FM Broadcast stations interfering with VHF reception.
Channel 6 is, for all intents and purposes, a "First Adjacent Channel" to the low end of the FM band. Those high-powered FMs are probably causing havoc there.
Channels 7-13 are, by design, almost exactly twice the FM frequencies....88 x 2= 176 MHz, 108 x2= 216.....the VHF High Band is 174-216 MHz.
It's likely that the RF tuners (the first stage of all receivers) themselves are generating second-order distortion when receiving high-level FM signals (they can also act funny when hit by strong signals elsewhere in the spectrum, but affecting different channels than 7-13). According to Charlie Rhodes, an RF expert and former member of the ATSC committee, tuners USED TO have an FM "Trap", or FM Rejection Filter, built right inside. That, of course, was in the days when TV sets were bigger, and the tuner itself was as big as a Christmas fruitcake.
As tuner modules became smaller, and more sets were used exclusively on Cable, the FM Traps went away. Many folks didn't need them (they were on Cable, or far away from FM transmitters), and the ones who DID need them probably didn't even recognize the symptoms of FM overload, so they didn't demand them.
Additionally, especially as it concerns the "Channel 6 issue", the low end of the FM band (adjacent to TV Channel 6) was restricted to lower powered stations (the so-called "Educational Allotments"), so there was a "buffer" between TV and FM. That is no longer the case, as high-power authorizations are granted across the band. Additionally, "FM Booster" and low-powered FM stations are often placed all over the map, not just at traditional transmission sites, so you might have a strong FM BCB signal coming at you from a nearby school, water tank or cell tower.
The long-term solution may be, to install an 88-108 MHz rejection filter ("FM Trap") on the input of each receiver, or at a point after the antenna, but common to all the sets. Very high FM signal-strength areas, such as those near the transmitter sites, might even require the traps to be placed right on the back of the sets and converter boxes, perhaps with some broad-band attenuation, too (bringing the levels of all signals back to their design-levels). Inexpensive filters cost less than $5.00, and attenuators can be had for a dollar or two each.
The 88-108 MHz FM Traps might cause some trouble with channel 6 reception though, just due to manufacturing tolerances, so a trap designed for 95-108 MHz may be better....IF there are few/no high-powered FM transmitters below 95 MHz. Otherwise, a tunable trap might be needed (in addition to the broader trap) to notch-out those particular FM channels. Something like that might have to be custom-manufactured for stations on a market-by-market basis, for cost and complexity reasons.
Trouble is, right now, the (88-108 MHz) FM Traps appear to be unavailable. The ones we have purchased are not available from the original supplier, and are back-ordered (for another month) from the only other (MCM Electronics) supplier we found. The 95-108's are available, though. Traps and attenuators used to be stock items at Radio Shack, but are discontinued, though you might be able to find them at local electronics shops.
The short-term solution may be for stations to move back to their pre-transition UHF channels until filters are available to the affected viewers (Or,... "fat chance" wise...., turn all the FM stations down to 10% piower).
You can read Charlie's article at the "TV Technology" magazine website, by clicking on their "Digital Edition", then going to pages 32-33 of the (current) June 10 issue. "Testing for DTV Interference" is the title.
The FCC is acutely aware of these VHF issues, although they may need to "research" the solutions before applying any "across-the-board fix".