In Adventure Mode you can basically not break any blocks, which includes the Noteblock. Only with the NBT Tag "CanDestroy" you can play the actual note of the Noteblock, but that also allows it to destroy it.

In Adventure Mode you can interact with a lot of stuff that is right click able. When right clicking a Noteblock you can change the pitch level of the note. So why should you not be able to left click it to play the actual note?

I mean you can put buttons next to it, but what about just punching it? The Noteblock is bigger and easier to hit and it can be very useful in Multiplayer mode and an Adventure Mode like area. And also it would make sense to left click the block aswell, if you can right click it.