...Given that there really isn't much in 5e to spend money on other than relative trivialities such as inn rooms and mundane gear, and given that 5e as written places very little emphasis on downtime between adventures, does the traditional "Thief" archetype within the Rogue class even have a place in the game any more?...
By the Thief archetype I mean the character who is the typical party Rogue while in the field but when in town between adventures pulls off a few 'jobs' or heists to enhance either its own personal wealth or that of the party; or who buys and sells information on the side; or who has contacts in many shady places the rest of the PCs might not want to know about...
Your starting premise is faulty. There is no more or less to spend money on in 5E than in prior editions. Go look at the PHB and DMG for 4E, 3.5, 3E, 2E, AD&D, etc.... People keep making this claim, but there is as much in the 5E books to support the use of wealth as there is in the prior editions. And even if you disagree and believe that there was more in the prior editions - so what? The things you spend money on outside of magic items do not require much rule support. You just need a good story to support the spending.
That being said, the thief/rogue has
never had a unique place. Magic is a better route to achieve anything a thief/rogue can do. Knock vs lock pick. Teleportation spells versus sneaking through a castle. Clairaudience/clairvoyance versus spying. You can summon up monsters that do the rogue 'acuisition' skillset better than the rogue. Dominate person plus modify memory is a real solid way to get away with almost anything. Heck... a lot of their skillset can be done by a non-magical barbarian:
Pick locks - with an axe to the door.
Stealth with intimidation: "YOU DON'T SEE ANYTHING!"
Disarm traps with extra hps.
The rogue/thief role is not there to fill an empty role - it is there because it is fun to play. It is an archetype from fiction that stands out and plays an important role in many stories - so we want to include it in the game - but to a large extent it is superflous when you have magic available. So do we need to fix it? No. Because you can't unless you remove magic.
This is the primary example I cite when I say that balance between classes and PCs in D&D is a fool's errand. If you try to give the rogue a unique role that can't be filled by a sneaky barbarian or a wizard ... well, you're either cutting off huge areas of design space from those classes, or your're failing. D&D classes do not need to be balanced. They need to be fun. Rogue archetypes are fun, even if underpowered.