I know part of it might be older folks looking back through rose tinted glasses and touting this time as an era "when real men played the game", but I feel like there is this weird moment where all of these sports went through a period of much more physical play-style than before or since.
The NFL play style was dominated by defense, and many teams such as the Steelers, Raiders, Cowboys, Giants, and Bears, seemingly won their championships on the back of legendarily tough defenses. This was also an era when a lot of NFL defensive players openly bragged about knocking guys out of the game and delivering huge hits, and it was an era that produced some of the most intimidating players such as Dick Butkis, Jack Lambert, Jack Tatum, Lawrence Taylor, and the entire '85 Bears defense.
Association football (particularly in England) went through a period when the game was very physical on the pitch. During the '70s you had the famous Dirty Leeds team that were notoriously physical, and the 70's and '80s saw the rise of hooliganism with took the physicality from the pitch and saw it reflected in the stands. Why did fans suddenly become so violent during this time?
The NBA during the 70s and 80s was a much more physical game if you ask anyone from that time. There seemed to be a lot more fights on the court during this era, and oddly enough even when fights broke out players would sometimes not get ejected. The 80s saw the rise of some particularly physical teams such as the Celtics, 76ers, and especially the Bad Boy Pistons.
Hockey is probably the one I know the least about. I know that fighting is just part of the game in hockey, but I remember reading that the '80s saw the highest rate of fights per game of any decade, and many see it as the era in which the goons were the most prevalent. Why did that happen?
American football might be the hardest one to judge because it is an inherently violent game, but the other ones seem to have experienced it. It just seems odd that all of these sports would go through a period of intense physical and violent play right around the same time as one another. Is it just a simple case of people being overly nostalgic for how the game was when they were young? Or is there actually some larger factor at play which led sports to be a bit more physical around this time? Or instead, has the extent of violent play just simply been exaggerated?
I imagine it's more that as the games evolved and became more professional more rules were introduced/enforced differently to protect players. I know that in soccer these rules were definitely beginning to be better enforced in the 90s, when the more technical style of the game began to take off in England. In rugby league in Australia similar rules started to be introduced in regards to the legality of certain types of tackle, on the back of some pretty serious injuries - this continued into the early 00s, with "spear" and "grapple" tackles being banned. Aussie Rules football also started to see certain tackle types being banned, and Rugby Union stopped allowing tackles while the opposition player was in the air, all as a result of serious injuries.
Another factor is making the games more "acceptable" (i.e. marketable) to segments of the population beyond the normal attendees (usually they wanted more women and kids through the turnstiles).
This article about off-field violence seems pretty good.