Steve,
You can use a light weight rod for more than just dry fly fishing. Keep in mind that if you purchase a light flexible rod that your casting stoke must slow down. As you tie one heavier flies like a size 10 bugger that this will change the workings of the rod and your casting stroke again. I cant explain how it does but it does. You will need to practice casting heavier flies to get the groove of it. I use a 3wt full flex and can throw a tandem rig of buggers with no issues.
Practice makes perfect, the best part about that is your on the stream when you practice ;-)
You can fish mid to large streams with a smaller lighter rod. However you must now consider your limitations (unlike flies). If you see a large fish and hook him, you are no longer just fighting the fish. Current can be an issue. You very well may have to plan your attack and landing ahead of time. Avoid strong current, you will lose that battle. Instead, you are are going to have to hook the fish and immediately try to get him to a desirable location. In my experience, the way in which you set the hook and pull will direct the fish for about 2 seconds. Once he gets his bearings and realizes something is drastically wrong, he will run.
Leaders are only a limitation (like flies) that come down to ability and practice. I use a 3wt 7 1/2 foot rod and often use 12 feet of leader and tippet. It takes practice casting leader almost double the rod length but you can do it.
Again, flies and leaders are not a limitation but a skill to achieve through patience and practice.
Full flex light rods are perfect rods for spring creeks. Like the Letort or Falling Springs. They mimic bamboo action without being bamboo or quite as good.
As you well know, there are multiple tools for multiple jobs. In the past I used one to do them all but I have found applications better suited for a different rod. Which is why my arsenal is expanding. If you dont own a light rod, buy one. You will enjoy it and find uses for it, just get one with a good warranty as they tend to break easier. Especially if you fish brushy, rocky remote brook trout streams. Brookie streams are hard on gear.
All this said, as far as trout fishing goes.....I believe a 3wt can be used on 95% of all PA streams. Your limitations are not as bad as you perceive.