Magento 2.1.2 Admin UI, multiple sites.
The general theme of this post is that on the Web Site config page there's a "Set as Default" checkbox with no indication of what it does. Yet experimentation shows that it controls or limits the Store (View) Scope that's in effect on some other pages, in surprising ways. The New Product page is an egregious example.
1a. As I note below, the "default Web Site" plays an important role in the scope of some newly created configuration. Yet the current state is very poorly shown in the admin UI. So far as I can see, the *only* indication is the "Set as Default" checkbox itself. Worse yet, once checked, on subsequent visits to the same Site config page, the checkbox is missing! So the only way to determine which is the default Site is to look for the checkbox that isn't there! This is surely a bug.
1b. The Set as Default checkbox needs an accompanying explanation of what it's setting the default *for*. It immediately follows a dropdown for "Default Store", which adds to the confusion. Though I've discovered one thing that the "Set as Default" appears to do, I really don't know what else it might do.
(As a side note, the Set as Default checkbox is not described correctly in the docs. I have filed a Feedback on that.)
1c. Even setting aside the disappearing aspect of the checkbox, surely the user shouldn't have to drill down into each Site to discover whether it's the default Site, and what it's default Store is set to. Instead, both of these settings could be very usefully displayed and selected on the next level up, on the Stores > All Stores list.
2. The New Product page doesn't show any control or indication of the Store View scope that the product configuration pertains to. In fact, it's not even apparent that one is establishing a site/store/view-specific product *configuration* rather than just globally-applicable product data per se. Only after first save does a Store View scope control appear, and then it offers only the Site/Store/View scope of the Site that was in effect at the time the Product was created.
So at that point the user might well discover they've created a product that can't be used on the Site they intended (despite having set the Categories appropriately). Worse yet, the user would have no clue how to fix this, or even why it got set up incorrectly.
Surely the New Product page could either show a Scope control, or at least show what scope is in effect, and tell how to change it?
(As a side note, this aspect of the New Product page is not described in the docs. I have filed a Feedback on that.)
3a. Actually, it turns out that buried far down the Product configuration page is an item "Product in Websites", using which you can select which sites the product can appear in.
Evidently, the action of the "Set as Default" Web Site is to pre-select just one of these Product in Website sites. (Checking an additional site requires also specifying where to copy data from -- a little unexpected unless versed in the process).
If you select one or more additional "Product in Websites" sites, then, after saving, the top-left scope selector will offer more choices.
Given the intimate yet subtle relationship between Scope and "Product in Websites", I think it would improve understandability to move the latter control a lot closer to the former, or to otherwise draw attention to their relationship.
3b. The Scope selector uses a lighter font weight to indicate nodes in the scope tree that can't be selected. Meanwhile, the Product in Websites "Copy Data from" scope selector uses a *heavier* font weight to indicate non-selectable nodes. Not fatal, just disorienting at the very time when it's already a surprise just being faced with such a demand for a choice.