Throughout different expansions and tiers, there have been different ways of progressing.
The first way was the Vanilla and BC way. No heroic bosses, just different tiers where each tier got progressivly harder. You had to gear up in the previous tier to move on to the next tier. You were known as a good raider by the fact that you had defeated Naxx or Sunwell bosses.
Next there was the Ulduar style, where each boss had a hard mode, but you had to do something different to do it. It wasn't simply clicking a button (except for a certain boss where you literally pushed a red button). XT for instance you had to DPS down the heart. Yogg you let the watchers not help you out. Basically the heroic modes had a little story behind them. This is similar to the protectors fight in the current tier where you kill them in a different order and get better loot.
Finally there is the style where you simply set raid difficulty to heroic, and the boss fights change.
If I had it my way, I'd mix Ulduar style with the BC style. Bosses have a hard mode, where you have to do something to enable it, and each tier cannot be completed until you defeat the previous tier. While this is obviously never going to come to pass, it's my preference. I do think however, that with LFR, players would still get to see all content, and this would bring back "progression" into the mix. The current system is a little boring.