Personal opinion: I just did a flip through a random scattering of my own VIs -- I found none where I would have room for even a second tab. I don't think this idea would help me much.
I'd suspect that even if it were just an option (as someone will inevitably suggest making it just as an option), a number of people would 1) Use it, because people love tabs. and then 2) Make their case structures extra large just to provide space for the tabs.
I generally frown on options to view diagram elements differently. It is the graphical language equivalent of having two keywords for the same concept. Sometimes it creates minimal disturbance -- like the long string or short string view of property nodes. Sometimes it would be completely baffling -- like the sometimes-made suggestion to let each user pick the data color for each type of wire (i.e. "on my machine, I want integers to be orange.").
This falls somewhere between those extremes, but it tilts toward the latter in my mind... minimal bang-for-buck while looking like a significantly different node and encouraging a different (larger) overall diagram layout. I wouldn't be hard opposed to it, but I'd need to see a lot of kudos before I'd think it was a worthwhile idea.
Here's a Quick Drop plugin that's not even close to what you're asking for, but it does let you see all of your cases at the same time - https://decibel.ni.com/content/docs/DOC-24058
Jim You're entirely bonkers. But I'll tell you a secret. All the best people are. ~ Alice For he does not know what will happen; So who can tell him when it will occur? Eccl. 8:7
Any idea that has received less than 4 kudos within 4 years after posting will be automatically declined.