That's not true. Strahan, Peppers, Taylor, Merriman, & Matthews lined up on the left side of the defense the majority of the time. Generally you'll get your premier speed rushers on the right side of the defense... Ware, Freeney, Jared Cook.
But it's not a hard & fast rule, sometimes you'll get a guy like Suggs, who isn't really a speed guy, but generally lines up on the right.
If Reed was any good at getting to the QB, the coaching staff would ask him to do more of it. It's no secret that we need more than just Watt putting pressure on the QB. If I saw Reed getting in on more plays, whether it be defending a pass, a TFL, a sack, or a hurry, I wouldn't have a problem with him starting on the team. But if he's just the guy who "sets the edge" we don't need to spend veteran minimum to retain his services.
Plenty of guys in the league who can set the edge & come off that block to get the tackle more often than Brooks does. Plenty of guys who can cover tightends & drop into zone coverage & actually break up a pass more often than Brooks Reed does.
If the coaches don't expect Brooks Reed to produce more than he's producing, we need new coaches.