How many decades have sports tried to eliminate PED's, and what have they achieved, absolutely nothing. Not because it can't be done, but because the sports themselves are corrupt from the inside out. Pro sports are about making money, and there's no money to be made if there are no PED's. Using every possible advantage to win is the driving force.
That is why other forms of cheating are not only allowed, they are tradition. For example, putting pacemakers in track races is cheating. It gives runners a physical advantage and allows them to go faster. It's as dishonest as a wind-assisted sprint. But it has been done for decades and results occasionally in records, which makes money, so it is allowed.
Imagine pacemaking being banned. There go all the European meets. No more sub 3:30's, ever. Nobody will watch track anymore. The sport would go broke.
That's the same thing that would happen if track really did eliminate PED's. Same for cycling. If performances regress, the sports will go into recession, and so the investors who set the rules and pull the strings see to it that PED's are not eliminated.
LA almost surely was a doper. Cycling protected him for a long time, but then USADA, for shamelessly self-promoting reasons, decided to put him against the wall, and cycling threw him under the bus. But cycling is not going to change one little bit. LA is just the fall guy for a tradition as old as cycling itself. As long as all eyes are on LA, they won't be on the sponsors and organizers who enable and profit from PED's, and they will easily figure out how to keep things as they are.
If you really want drug-free sports, you must decide if you can do without the sponsors and the big money. There won't be records anymore. There won't be many good competitions. They won't be putting it on TV. It'll be crap. PED's are cheating, but that's how it is. Cheating's traditional now. You won't recognize the sport without it.