5E does treat gold acquisition and expenditure differently than say AD&D. And depending on a person's particular playstyle, that could be seen as a bane or a boon. No one way is better or worse than the other, it all comes down to personal preference on how important wealth is to the game.
I don't find the archetype, as you detail it, to have been particularly strong. While folks like the image of the thief who goes off on their own and does crime, the game has never really supported it well - both in basic tactical terms, and in the meta-consideration of GM attention, it has issues.
I think these allude to what I was going to say.
5e is very much like 2e AD&D -- there are options there to make gold be meaningful, but if the DM or party do not engage with it, it can be rather meaningless. In both cases, it was a reasonable decision -- a significant subset of people didn't have an interest in perpetually running the raid-the-deadly-hole-in-the-ground-for-(non-magical)-loot play cycle (nor necessarily the keep & army use for the gold once you acquired it*), so easier to make the acquiring of gold an optional activity than keep gp=xp front and center.
*to say nothing of AD&D level-up training costs, which I think lasted one summer for my main group.
Also very much like 2e, I think Umbran is right -- I think more people included the thief imagery and motif than spent a lot of time doing direct thievery. The Thief class always seemed more like what Backgrounds now cover -- the backstory of what the character
used to to do that gave them the skillset that made them a good lockpicker and trap-finder that they now mostly put to use in dungeons. I definitely know that when
The Complete Guide to Thieves came out for 2e, everybody lined up to look through the kits and stock up (using their otherwise unspent gold) on dog-pepper and tar-paper and hidden wrist-sheath daggers and boots with hollow heals and all sorts of other fancy equipment designed for civilian burglary and the like and... never quite got around to using them much.
Even in editions where money clearly is important (the xp=gp ones and the WBL-magic-item-purchase ones), generally the money is more often acquired by group adventuring than individual Rogue/Thief thievery capers. The rules have been just too punishing on the one party member out on their own when their hide/move silently check fails, and there's too much in the game world that doesn't care that you can hide well and find physical traps and such (and of course the rest of the players don't want to sit on their thumbs while the 1-2 party Thieves go have a side adventure). Games that thrive on this type of adventure (Blades in the Dark being the fan favorite these days, I believe) tend to work because everyone in the party is a rogue-character and the challenges they face are the kind addressable by a rogue (or occasionally rogue-ghosttalker).
So, yeah, I think 5e is carrying on a long tradition of the game including 'thief' characters who are really more adventurers who once had thief training. Of course, the magic user/mage/wizard characters have long been 'scrawny grey hairs who spend every waking moment studying to acquire power' that don't actually spend much time studying (except re-preparing dungeon-raiding abilities), and gain most of their power raiding dungeons. Of the archetypal classes, only fighters (who certainly do do a lot of fighting) and sometimes cleric/paladins (with varying degrees of system-enforcement) seem to have had much focus on them doing the things they are iconically 'about.'
