Since money really is power in D&D, what sort of wealth-to-level gauge should we be using?...The goal is to come up with a relatively objective scale by which we can measure PC power relative to their levels.
No such simple scale exists, because there is no good conversion between money and utility. Even assuming such a scale could exist, it would first require you to tweak the existing magic item cost/magic item creation system so that items were well balanced according to price. And even then, you would need an assumption that players had the will and ability to maximize their utility given the resources that they have. And that requires that you have fungible wealth, meaning that whatever the players find, they can freely convert it into the items that have the most utility for their character.
For example, supposing that magical weapon prices are well balanced, the part discovers a two-handed sword +5 - worth ~50,000 g.p. If the party contains a two-handed weapon wielder like a barbarian or a fighter specialized in the two-handed sword, then that additional wealth does reflect additional party capability. But if the party is entirely spell-casters without martial weapon proficiency, then the weapon represents a great influx of wealth on paper, but in practice little or no increase in their capabilities as a party.
The situation gets worse with respect to items that are poorly costed which includes pretty much any use activated item that grants a spell effect or buff that is probably underleveled - fly and invisibility come to mind immediately, but there are many others. In particular, watch out for buffs that last rounds when cast as a spell, but become permanent when in an item, or buffs that are quickened when on an item (free actions). They are all undercosted in stock 3.X, because stock 3.X doesn't price in the value of increasing the duration of a spell. And of course, there are items where the cost system works fairly well, but are circumstantially broken- the most famous of which is the wand of cure light wounds.
Depending on what exactly the wealth translates into, you get completely different adventuring utility. If the PC's inherit a cabbage farm, a cottage, a cart, a mule, and two oxen, that might add up to a magic item in value, but not in (immediate) utility. Equally obviously once it's stated but perhaps more easily overlooked, if the PC's have 2000 g.p. in their pockets, they have not increased their utility at all - indeed, all that encumbrance might mean they've reduced it.
That's why I state that I don't bother to follow wealth by level, and rely on the older system of semi-random treasures and keeping an eye as a DM on party capability to make sure that they have enough items to face the challenges they are expected to face. That means noticing when a party member is falling behind, and placing treasures of great utility to them in their path, and conversely drying up the treasures when a party member starts to look overly optimized in their gear. The value of the gear isn't something I spend much (or any) time considering at all. It's the utility that matters.