Multi-row tabs are the primary thing I dislike about old UIs. You never seem to see them anymore, for which I am immensely grateful. Not only do they take up valuable vertical space, but they way the rows jump around always confused more than it really should have - a button shouldn't move after I click it, especially if it is representing state.

My (admittedly spontaneous) thought was that we don't see them anymore because flat design make them almost impossible. Even with dividers, it would just look like a grid.

I don't think that more-tabs-that-can-fit-on-one-"line" is ideal, but I think the modern equivalent - horizontal scolling tabs - is waaay friggin' worse. I've been confused by those before whereas the first time I encountered multi-row tabs in the "depth style," I had zero confusion about what I was looking at.

As opposed to tabs that either (a) get so small they're illegible, or (b) scroll off the screen so they're no longer accessible?

The moving tabs issue we can fix but just not moving them.

And the vertical space issue is much less of an issue now than it was then because we have higher resolutions but the answer to that is to start closing tabs when you can no longer see your content. It's like a quiet little nag that says you have too much stuff open.