I had meant to comment on this when it first came up, but alas, there is other life for me outside coins (I know, hard to believe, but I can multi-task. Watching the Olympics now and writing this, also conversing with the kids, cooking dinner, etc.). I think the debasement of coins likely was no different from the modern. The government simply makes the change, none of us can don anything about it. Before, coins were near pure silver, then gradually debased until they were just washed with silver. At that point (as already pointed out) they were fiat. And what difference did it make? None. As long as people were still willing to exchange these coins for goods and services it all worked just fine (as did with modern monies). At this distance in time, as @Alegandron pointed out, money is just a concept, just bits and bytes and nearly completely electronic. So many of us just use Paypal for may transactions, which is entirely digital. As long as we all decide it is OK, well, it is just that. OK.
The silvered coins were supposed to contain their face value in silver but at debasement of 20:1 the was was needed to remind people that the silver was in there. They could have chosen to issue tiny silver coins or much larger copper ones but they took the middle road. The amount of silver on the surface was not much compared to the 4.77% hidden inside. On occasion we have evidence of the mint cheating and delivering less than expected making the coins as worthless intrinsically as paper money. We even have records of Aurelian cracking down on his mint workers for profiting inappropriately. https://en.wikipedia.org/wiki/Felicissimus
I used to do an Origins of Money talk for my kids' classes when they were in 3rd grade. Part of the discussion was intrinsic value of the material money is made out of. To illustrate intrinsic value, I held up a $20 Federal Reserve note and a $20 1924 St Gaudens double eagle and asked if anyone would prefer one over the other. They're both $20 so why care? Everyone picked the gold. Even children know we've been screwed with paper money. The teachers never knew that gold was real money at one time.
As a retired history teacher I can tell you that, indeed, my teaching colleagues, including those who had majored in history, knew virtually nothing about money except for what might be in their pockets. Even my professors, and this is going back some time, knew little about coins or currency, so it is no wonder their charges, future teachers, would know so little. Had I not started collecting as a youngster I probably would have been one of those ignorant ones. Even most learned and published historians frequently make egregious errors in their writings when it comes to coins and currency. When it came to my own students I would often bring in the money of the period I was teaching, explain what it was (and they ALWAYS asked "how much was this in our money". Most were quite interested, especially when they realized the value came not from government decree but the intrinsic metallic worth, except when government debased or printed its way with fiat money. What was most captivating was when I told them that the Athenian Owl they were handling (I passed the coins around the room) might have been spent by Socrates, the denarius by Julius Caesar, the English Long Cross silver penny by Edward Long Shanks or the British gold Guinea by Ben Franklin. By the time my students hit the 20th century they knew what "free silver" and a Cross of Gold meant for the US economy and when FDR took the US off the gold standard they knew why and what that meant for the depression Era economy. I think there are a few adults out there who do have a fair idea of what underlies economic policy and if they do, it is more likely to come from numismatics than business schools. By the way, I did the passing around of the coins for over forty years in my high school classes and never once had any missing at the end of the day.
Not tin, its actually silver. From what I have read, we have a decent understanding of how they did it. Make a copper planchet with say 5% silver. Now soak the planchets in salt water for a period of time. The salt water will leech out the copper atoms on the surface of the planchets. Take them out and strike them. Since the surface is not silver rich, the heat of the strike will cause the silver to melt and coat the outside with a thin layer of silver. No magical plating required, and the populace gets to lie to themselves that the government coins aren't debased. A friend strikes coins for medieval festivals, and has tried this. He said its not as good as the Romans achieved, but it did coat the coin in silver. I am sure the Romans, with all of their mints, got it down to a science eventually.
My observation is that this problem extends far beyond money. The past was a very long time and included several hundred areas of special interest to a few that were pretty much ignored by the majority of 'Rome fell in 476 AD' book writers. Unfortunately current requirements to teach to the test and judge the success of a teacher/school by standardized test scores helps nothing. I wish I could figure out how to test students for the level of their inquiring minds or belief that it is more fun to know than not to know. I do see hope for the future in the fact that being a geek is more cool today than it was when I was a kid.
My experience of grad school for history teachers was that it focused on teaching methodology to the extent that there was little time (or interest) to teach content. I figured out pretty quickly that if I wanted to increase my content knowledge of history I needed to do so on my own. That meant copious reading, frequent trips to historical sites, joining two historical reenactment groups and becoming a docent at a museum of history. Still, on the money issue, nothing gave me the necessary understanding of the role of money in history better than numismatics. Wherever I went, taught, guided or wrote I was usually the only one there who understood the "why" of fiscal policy.