Any detriment to hanging a bike by its front wheel?
You'd have to calulate the actual forces to be 100% sure but it's not going to be a problem: forces on front wheel/fork/headset while e.g. just sitting on the bike, braking or landing jumps will be (much) higher than the force applied from hanging it.

That being said, I do note at least two problems with this setup: first, good luck getting one of the center bikes out without touching or getting stuck in another bike. Second: from the picture it seems like you'd have to hold the bike with one hand then use the other to attach it. Ok for a roadbike, but for anything heavier that is just hard. Usually these systems have an open 'C'-shaped fixed hook into which you simply hang the bike which is much more convenient.