I agree that it could have neen worded better, but I think you overstate the brokenness of it.
Well, "brokenness" is your word. I think the spell is problematic. I think the designer realized just how problematic it was and that's why they wrote in the aside about the GM being able to control the destination of the spell by fiat. However, I think the designer overlooked the issue of secrets, because the aside (almost a sidebar in the middle of a spell description, which is odd in itself) makes clear you can't planeshift to exactly where you want to be but does imply that you will always get near to where you are going. And that may not be "broken" but it definitely is a problem, and the OP is right to point out how much of a problem that is.
If you want accurate travel within your own plane you need teleport. Even then, you need very specific knowledge to get exactly where you want to go.
Or you could just planeshift twice, once out of the prime, and then once back to the prime. You'll get close to where you want a go with no chance of mishap or failure, and you don't even need specific knowledge of your destination. Don't know where the Tomb of Horrors is, or even what it looks like? No need for investigation and exploration, as long as you know what plane it is on, just cast a spell and you'll be in viewing distance of the tomb.
With plane shift you can get in the general area of a place you want to go but the text gives a lot of leeway to the DM.
Some leeway, but not enough to hide a secret.
First off...how hard or easy is it to acquire the material components?
The tuning fork is not a new element of the spell. It's been around since 1e and I can tell you how this works in practice. As long as the plane isn't a demiplane, for a character of the level that can cast this spell, acquiring the material component is trivial. As I said earlier, the tuning fork material component exists only to allow a DM to hide an entire plane and force investigation and exploration in order to get there. But for well known planes the tuning fork requirement is a trivial investment in high level resources.
As for using it to find a secret location on the plane they are on...that seems to me to present its own set of interesting problems...once they get there, how do they know where they are in the world?
Does it matter. When you have instantaneous pinpoint travel you no longer have to worry about spatial relationships. Everything is adjacent to everything else. Travel by map is no longer needed.
I think you are giving the spell more power than it has. The text implies you cannot use it to get to a specific location...only general, and even then the DM has a lot of options available on how accurate he wants it to be.
Again, you are ignoring my complaint, and going off and arguing your own bit. I agree that the designer with his DM fiat side bar in the spell description made sure that the spell could not be used for exacting travel. You can't guarantee like you can with teleportation circle you land next to where you want to be. But his sidebar didn't give by rule DM's enough leeway to determine where you land. The implication is you still always get to where you are going at least in a general way - the worst case example in the text is within viewing distance. I think the designer thought this empowered the DM enough, but quite clearly it doesn't.
Considering what my players have been willing to do to make sure Teleport is reliable, I can't imagine they would even consider Planeshift to get into any hostile location if there is some other reasonable way presented to them.
Yes, but Planeshift can get you to - as the OP's PC realized - a completely unknown and secret location. And that seems to run contrary to the design of all the other spells in the book.