I still have the wheel in the back of my logbook to scare instructors, although any recently minted instructor wouldn't have a clue what it is.
I still carry my wheel with me on trips. I don't use it except to get on the boat, get my wheel out, and ask the Dive Guide (with my wheel visible) something like "We are going to do multi-level dives, right?" The looks that I get are often worth the price of the dive. Then I'll break out my computer and back-up computer and everyone has a good laugh. It doesn't mean that I know diddly-squat about dive planning or diving at all, but I have a computer so they are happy.
Having drilled hundreds (maybe thousand(s)) of students on the use and understanding of the tables back in the late 80's and early 90's, I have (or at least had - I'm getting older) the tables pretty much memorized (both sides). Being a mathematician, I am pretty good with numbers, and I still am constantly recalculating bottom times when I'm doing rec diving with a non-square profile. I use a "base" number and then use a + or - calculation based on time/depth. It's VERY rough, but I can come relatively close to my computer. This is all based on tables.
With that being said, I am learning to relax my brain a bit these days and just check my computer from time-to-time. If something doesn't look right all of a sudden, then I would assume that the computer COULD be malfunctioning and check the other computer. It hasn't really happened yet, so I just keep THAT plan in my playbook.
I don't think that someone HAS to know how to use tables before they use a computer, but I DO think they MUST know the concepts the tables or computers are designed to be use for.
None of this really addresses IMHO what is the important thing about using a computer OR tables, and that is on-gassing and off-gassing and what's happening to your body when you dive. Again, IMHO many newly certified divers have little or no concept of what is really happening when they are diving, and DCS is some semi-mythical illness that only advanced divers get because they do decompression dives. Just for fun, the next time you are with a group of people on a boat or similar place, ask someone who appears to be new, or even an oldie, what's happening or has happened when a diver get hit with DCS. Ask them in a way that you are trying to get a better understanding of it and want multiple explanations. If they don't know, it may be a brief teaching moment. Another question to ask is "How many compartments does YOUR computer consider in its calculations? Mine uses X". These questions are not meant to be judgmental. It may alert you to someone you might want to watch if you are a dive professional. There are all kinds of ways to determine if a person understands what is happening physiologically when they go diving. I think it's something we should ALL know or at least have a fair understanding of.
Someone earlier said know how to use the tool that you use. That is important. More importantly, IMHO, is why are you using this tool? What does it really tell you?
I agree with the idea that the recreational dive industry is based on numbers. It's almost like a pyramid scheme. The people at the top who are getting a slice of every pie are making money. The guys in the trenches (instructors) for the most part.... not so much.
Before everyone jumps on saying how wrong I am about this point or that point, just remember, this is MY OPINION. It's probably not worth the paper it's printed on.
Cheers -