I hear you on that. But that's one of the reasons for signing up ahead of time for these tours. We have time slots so theoretically no lines. And the DC stuff doesn't cost anything... just some paperwork and requests ahead of time.
You don't have to do this for the statue of liberty - unless you want to climb to the crown AND avoid the lines. You have to pay, regardless if you arrange ahead of time or not.
Pre-booking what you want to see works well. It's a great way to avoid the lines. And we only do this for things we really want to see. The way I look at it, there's two different ways we vacation. We are either site-seeing or exploring. If it's site-seeing, then I try to come up with some plan of what we want to see and pre-book as much as possible. If we're exploring, then we might have a list of things we want to do, places to see, but figure it out when we start the day depending on how we're feeling.
We went to DC/NYC last summer. DC was great because it didn't cost anything to see the attractions and there are ton to see. We were limited on time, so we hit the highlights, but I wish we had an extra day so we could have biked along the Potomoc, probably to Mount Vernon. If I was doing it over again, I'd figure out a way to squeeze it in.
We went to the crown at the Statue of Liberty and it was worth it. I was surprised at how little space is up there. We were lucky, or maybe it's intentionally spaced out, but there was nobody behind us so we didn't need to rush down after we got up. There are national park rangers staffed in the crown, which gives you the opportunity to ask questions, etc.
The highlight of NYC for me was The Met. The Modern and Contemporary Art collection was fantastic. You can easily spend hours going through the museum. The 9/11 Memorial was well done and also worth seeing. On our last day, we went to the Brooklyn Bridge. If we had more time, it would have been nice to walk to the other side. And earlier that day, I took a solo trip to see the HighLine. Nobody in my family wanted to go so while they were still busy getting ready in the morning, I went to the HighLine (through Chelsea Market) and walked it for a few blocks. I wouldn't necessarily go out of my way to visit the HighLine, but if you're in the area it's worth seeing.