I just finished reading the book "Steriod Nation" by Shaun Assael and to say that it was an eye opening look into the use of steriods in the past 30 years would be a huge understatement. I'm not here to give a review but to give you a short answer to the question posed by this title based on what I've learned from this book: Not any time soon.
It's not a simple matter of stricter testing or more testing. Tests are only as good as the person doing these tests. Urine samples are fed into a machine called a gas-chromatography/mass-spectrometry Machine . This machine heats urine up to several hundred degrees and this machine in turn reads the chemicals that are in the steam. It's up to the scientist or doctor to be able to look at these chemicals and tell what they are. Some steroids, such as dinabol or stanozolol, are very easy to spot. Other's chemical signatures, are more difficult to spot. Some resemble other hormones, such as birth control pills. In essence, it's just as important to be a good detective/investigator as it is to be a doctor or scientist. Otherwise, something can be missed. This is what people like BALCO's head steriod sylists Patrick Arnold was very good with getting away with.
One of the sporting world's best steroid hunters, Don Catlin, was very good at spotting steroids. One time, he was able to catch a notorious doper in the Cyling world not because of what he did see but what he didn't see. This is where being a good investigator comes into play. She had practically NO testosterone in her body, which is highly unusual even for a woman. This is how he discovered that she was using the latest, greatest "undetectable" steriod. Still, he had a bit of trouble making a case. Charges like this can, at times (not this time however), be hard to stick because the tests so cutting edge that the lawyers will argue that such a positive test amounts to an experiment and not sound science.
There has been a call for a system in pro sports in which an athlete gets a through bloodwork to measure all of their hormone levels on a regular basis. This information is then stored in a file so if an athlete's testosterone ratios change radically, it can be used as a sign that this person is using steroids. Would it surprise you that this ideal is wildly unpopular in the sports world?
Still, there's another problem. Many of these "youth clinics" or "anti-aging clinics" are really just a front for people to get steroids for performance enhancement. They won't go overboard and give out Lyle Alzado amounts of steroids. Instead, they'll measure testosterone levels in the client's body by comparing the testosterone to it's precursor, epitestosterone. Positive tests for testosterone are often found because the ratios are outside of a legal range (usually 6 to 1). If the client is only 1 to 1, they'll administer only enough to bring them up to the legal ratio. Had Floyd Llandis had modestly high ratio rather than the 11 to 1 he pissed hot for, he may have gotten off by claiming to have naturally high testosterone levels.
So, from the investigative level, doping is very hard to catch. The even bigger problems are HGH and Insulin. They have no reliable tests for either yet. New drugs come out all the time, requiring a keen eye to spot them. The biggest problem of all though is that the sports world doesn't want to catch anyone. Random testing is a pariah in sports. Corruption leads to lost paperwork needed to match sample numbers to actual names and other dirty tricks. Rarely to the doper-hunters get the facilities they need to do their work. They are given little consideration in law enforcement because they are seen as less of a problem than harder drugs such as cocaine or herion. As a result, prison sentences are much lighter for steroid users and dealers.
The reason is simple: pro sports make huge money when athletes use steroids. In spite of the scandal involving baseball, attendance has done nothing but go up. The increased size and strength due to steroid use by NFL players lead to its rapid increase in popularity in the 1970's. Lance Armstrong was long suspected of doping. Did anyone watch or care about the Tour De France before him? The sad truth is that the world LIKES watching doped-up players.
The only way that we'll ever get rid of steroids in pro sports is when the audience gets sick of it all and stops watching and buying tickets to pro sports. Catching them doing it is a tough game that even the best have a hard time winning. It has to become unprofitable for pro sports to feature steroid-laced athletes. So far, the exact opposite has happened. So, steroids in sports will be around for a long time.