What the hell are you guys arguing about?
There are basically 3 beta profiles I think everyone is confusing here. Two for iOS (public and dev) and one for the watch (dev only). Both of the iOS profiles can be installed on the watch but won't do squat, they will NOT invoke a beta update. However installing the watchOS dev bet profile to the watch will.
Months ago, someone shared the watchOS and iOS 10 dev profiles publicly and people were able to install the watchOS betas on their devices. I'm one of those people. I think some of you are confusing the iOS dev beta and installing it on the watch and confused why it doesn't do anything. It shouldn't, it's for iOS. But I promise you, the watchOS dev beta does indeed grant you access to the dev beta watchOS versions. I myself are and always have been running them and I'm not a dev.
Coolbreeze, you are installing the iOS beta profile to your watch. Of course it won't work. The only misunderstanding is your assumption that this profile will do something for the watch. It won't. And the fact it won't isn't because it's "restricted to devs only" it's because it's not the correct profile. The profile is available in the public beta page because it's for public iOS beta testers.
Just because the round peg fits through the square hole, doesn't make it a square. You have confused two different profiles.
Below is what the watch profile looks like, installed on the watch app. Clearly, different than yours. To the watch and the phone, a profile is a profile. It doesn't discriminate what it's installing. As long as it's an apple verified profile, it will install. What it does on that device will depend on the hardware. An iOS profile on a watch won't do anything.
Edit: after rereading your thread, looks like you grasp the concept I just reiterated. My guess on your question is that as I stated, Apple devices see the profile just as that.....a profile. It can't understand the name of the profile and prevent it to install on an incorrect device. All it knows is it's a valid profile and installs it. Guess they depend on people being smart enough to install the correct profile on the correct hardware.