The 7-7-7 rule was a staple of broadcast TV that lasted from 1934 until the era of deregulation in the 80s. It is indeed the rule that limited any single entity from owning, OR CONTROLLING in any way, more than 7 TV, 7AM and 7 FM properties. This rule also prohibited any single entity from owning or controlling more than one of each in any single market, and a single entity could not own a newspaper and a TV station in the same market.
The reasons from these rules were
1) to encourage localism (local ownership) and have stations serve their communities better
2) to encourage editorial diversity. No one entity had a stranglehold on any market or region so different editorial POVs were at least theoretically possible.
3) to ensure that the most number of entities (people/corps/co-ops) had the opportunity to use a very limited resource.
Part of these same rules prohibited any one entity to own or control more than one TV or Radio network. ABC network exists because NBC was forced to sell its Red Network (there used to be the NBC Blue and NBC Red radio networks.) NBC had a stranglehold on radio (the only electronic media at the time. CBS was the only viable competitor and it was struggling.
It is no coincidence that the prices of TV and Radio properties shot through the roof in the late 1980s as there was a feeding frenzy by media conglomerates buying out every broadcast property they could as fast as they could. It is no coincidence that local ownership of major broadcast stations (both radio and TV) is nearly non-existent now.
I would be remiss to leave out some positive effects of the relaxation of the rules. One is the explosion of so-called independent TV stations in the 80s making way for the possibility of competing networks like Fox, PTEN, Action, and other Syndicated programming (Like Star Trek TNG) that would not have found room in the established networks.
The ownership restriction rules were relaxed in stages through the 90s to the point where they are nearly useless now. They have more to do with audience share per market (for local stations) and nationally (for networks). The network ownership/control rules are idiotic because it essentially ensures that an entity's second network is poor performing, non-competitive junk! See: CW, Ion
The reason for ownership rules is just as relevant today as it was when they were in place. If anything, these last three decades show exactly why ownership rules for the limited broadcast resources were needed and still need to be imposed!