These won't all necessarily hang together, but I wanted to put them out there in hopes others would have other angles to add or better references.
1. Performance Enhancing Drugs (PEDs) in sports is only one part of the picture; PED research in the military (or better, just PE, as drugs are only one form of military PE) is probably more advanced. The reports in Jonathan Moreno's Mind Wars (2007) are probably long outdated, but it is at least a start on the outlines of the issue.
2. PED experimentation in sports and in the military (and in the arts, for that matter) are intertwined with, and often the leading edge of, commercialization of drugs for general consumption; consider the recent consumer-targeted ads for "Low T," or more generally the "anti-aging drug" business.
3. The increased number of US men who desire to "get big" received a big boost in the 1980s with the release of "hard body" movies.
4. The logic legitimating the PED chase seems to have two parts. First, PED use coerces competitors into using drugs that may damage their health. They don't have to take the drugs, but if they want to be competitive, they do, so this is dangerous coercion. Second, PED use by adult sports figures tempts teenagers into using drugs that might harm their health.
4a. It is possible that the bad health effects of androgenic steroids have been exaggerated:
When examining the potential medical issues associated with anabolic steroid use, evidence indicates that most known side effects are transient. More so, few studies have been able to directly link anabolic steroids to many of the serious adverse effects listed. Although clinical case studies continue to link anabolic steroid administration with myocardial infarct, suicide, and cancer, the evidence to support a cause and effect relationship is lacking and it may be other contributing factors (i.e. genetic predisposition, diet, etc.) play a substantial role and potentiate the harmful effects from anabolic steroids. Consistent physician monitoring is critical to the athlete who consumes anabolic steroids. However, many athletes may not undergo extensive medical exams prior to androgen administration and few physicians may be willing to provide such monitoring.
©Journal of Sports Science and Medicine (2006) 5, 182-193 Review article
MEDICAL ISSUES ASSOCIATED WITH ANABOLIC STEROID USE: ARE THEY EXAGGERATED?
The College of New Jersey, Ewing, NJ, USA
4b. I do think it's the case that steroid use by teenagers is dangerous, since their hormone regulatory systems are not yet mature. But then the question becomes whether there is any good evidence that teenagers do steroids because of the publicity given to prominent sports stars. This would be very difficult to disentangle from a general desire to "get big" and be strong (see point 3 above) and be a better performing athlete / recover from injury. Of course the cultural desire for teenage boys to "get big" I suppose is partially attribuable to celebration of sports stars, but it would be hard to show exactly what's going on here. Of course exactitude is not to be expected in all areas, as our friend Aristotle would remind us!
5. Here's another angle: it seems that football players are much bigger now than 20 years ago (here's an unscientific survey; but this study nuances the situation). But are we sure steroids are the reason or even one of the main reasons? It might be that players are bigger just because they are lifting better (i.e., heavier weights starting earlier in their lives) and stuffing themselves with food (and supplements). Large size can in itself be associated with bad cardiovascular health effects. (The concussion / brain damage issue is complex; recent thought tends towards linking CTE and repeated low-level subconcussive events. So it might not be increased mass so much as lots of "regular" hits in practice. Which is why the NFLPA negotiated a limit on contact practices in the last contract.) So it may be that the focus on steroids distracts us from the bad side effects of the body mass results of current football training regimes simpliciter.