You could easily tie spending gold into the DMG '14 Renown system, and since one of the suggested benefits of Renown is access to magic items, in a world without magic shops and random rewards this might be the best/only way to get specific items.I like the previously mentioned using money to increase your reputation. Doing so could open the doors to more profitable adventures. Now instead of merchants hiring you, nobles hear about you and seek you out. Not sure how that actually can play out as you don’t want to gate adventures behind reputation but having more profitable jobs or having access to fancier things or more influential people can be useful for all kinds of things.
Similarly there's a Piety system from the Theros books where you could easily attach a gold cost as part of gaining piety or possibly just to advance to the next threshold.
Having quests have renown/piety requirements does make some sense especially for non-time sensitive ones. The famous explorer planning to find the lost city of gold won't hire you unless you have a big enough reputation even if that means they are effectively waiting around for weeks/months for the right folk to hire, after all it's not like the lost city is likely to be found, especially if the famous explorer has secret knowledge about it's whereabouts.