You're right, this
is confusing. After some consideration, here's my take:
By the time the mid-game rolls around, Gold is too easy to come by, and there are often relatively few things to spend it on. That is, Gold has too little value. The marginal value of Gold (how much would 1 more

help me?) is too low. The budget constraint does not have enough "bite" (is not sufficiently binding). These are all different ways of saying the same thing.
The solution is to either
(1) make Gold harder to obtain by reducing tile yields or bonuses ("contract the money supply"), and/or
(2) make things [maintenance, units, RAs, etc.] more expensive ("raise prices").
The first makes Gold more valuable because in Civ, as in real life, the marginal value ("marginal utility," in economic terms) of money is declining: going from 0

to 200

is great, but going from 8000

to 8200

isn't much of an improvement at all. It's a bit trickier to see (hence the rest of this long post!), but the second makes Gold also more valuable – because you'll run out of it more quickly.
The thing is, Civ V does not represent or approximate a market system, so much of Econ 101 thinking doesn't apply. Prices in this game don't change as players' supply and demand change (except arguably with

Influence for City-States, but not really even there – certainly not in practice in single-player games, since AIs hoard money for no reason). In fact, we're directly setting prices (doesn't happen in markets!). What's going on here? Here's a thought experiment:
A) Everything is free. Units cost 0

each to buy, everything costs 0

to maintain, etc. Obviously, here, each unit of

is worthless, and having 500

is just as good as having 50,000

... if, for instance, we were suddenly offered the chance to give up 999

for 1

, we'd do so in a heartbeat.
B) Everything is arbitrarily expensive. All units and buildings available for us to buy cost 999,999

each to buy, 999,999

per turn to maintain, RAs cost 999,999

, etc. Now anything we'd want to spend our money on is completely inaccessible to us, so each marginal unit of

is worthless. If offered the chance to, again, we'd definitely trade 999

for 1

.
Obviously, in between these two extreme points, each unit of Gold
does have some gameplay value (i.e., having more

makes you more likely to win). Graphically, we have something like
, so the relevant question is whether we are to the right or left of where that function hits its peak, C. To the
left of C, things are so cheap (i.e., close to free) that we can afford pretty much everything we need, and so there's not much to do with what leftover Gold we have: if our treasury doubled, we'd shrug. To the
right of C, things are expensive enough that we're still getting a decent amount of bang out of every last dollar (well, unit of Gold) that we have available, and every Gold decision is a hard decision because there are tons of things to spend it on, each of which would help us greatly, and it's hard to see what the optimal choice is. If our treasury doubled, we'd jump for joy.
In the early game, this latter situation holds (e.g., good play dictates selling resources to the AI for Gold, we agonize over what to buy – a Temple? Catapult? A CS ally?, we're anxiously watching our treasury to see when we can afford that Settler*, etc.) But eventually, it's quite clear we end up the left of C, at least from my experience: once we have our core cities up and our economy is humming, Gold is pouring in from all sides and there's not much to do with it other than dumping it into Research Agreements and City-States. So prices need to be higher (so that we spend more money on stuff we really need, making our budget constraints more "binding"), or Gold needs to be harder to come by (so that our budget constraints are literally lower and therefore more binding).
* – this is why I don't like that Opportunities require cash on hand as opposed to having costs implemented by something like per-turn

/

/etc reductions, by the way. Having a single, literally random incentive to keep money in the bank fills Gold management decisions with angst, and not the fun kind (which would be something like the anxious "what to buy?", "right of C" situation described above... in fact, it takes these desperately-waiting-for-enough-gold situations away).
One last illustration: when playing as Spain, you're way happier finding a NW and snagging the 200

prize on turn 20 than on turn 200, right? This
isn't just because units and buildings are more expensive by that stage. It's because our economies' growth in between those turn far outpaces the growth in prices of age-appropriate units, buildings, and their maintenance. The key issue is the marginal utility of money, which comes out of both the level of prices
and the availability of money.
[
Technical aside: In fact, fixing this problem probably requires a significantly
larger adjustment to the money supply and/or prices than it might seem at first glance. Suppose we had tons of data on skilled VEM players and we find that, on average, a gain of 1,000

increases our chances of winning by 0.5% on turn 100 but a full 1% on turn 75 (assume for simplicity that no new units/buildings become available between these turns). Then gradually increasing prices so that turn-100 prices are double those of turn-75 prices would solve the issue, right? No, because in reaction to this price change, players would reallocate their Citizens/arrange their Cities to produce more Gold and less of other things. In fact we'd need prices to
more than double between turns 75 and 100, even if no newer/better units and buildings became available during that span.]
A different but closely related issue is that Merchants are rarely worth employing. Dealing with the above problem (making each unit of Gold more valuable) would definitely help this, and for all I know could pretty much nail the issue. But I've always thought Great Merchants, even after all the VEM buffs, simply weren't all that fun to use. That's what my earlier suggestions were trying to deal with; I should've been clearer. In any case, the value of Gold issue is obviously more pressing, and in fact may in fact be the only problem here (in the sense that dealing with it may neatly and automagically fix the Merchant vs other Specialists balance issue).
Anyway, enough with the theory. In terms of what should change, I'd suggest
- mid- to late-game RAs need to be more expensive relative to units and such (as has already been done! The last game I played was v130, so I don't know what the new higher prices feel like yet/whether the increases were too little, enough, or too much),
- mid- to late-game maintenance costs need to go up across the board (esp. buildings: wide empires always seem to be flush with Gold. Can building maintenance be made to depend on population, by the way?),
- CS bribes/"gifts" should cost more late (they're expensive enough if not too high at the beginning of the game, but nowhere near high enough later... but I think I remember you saying this was unfortunately hardcoded into the game),
- Gold buildings like the Market and Bank may need to be nerfed,
- Golden ages should give less of a Gold boost, and/or
- Gold tile yields [for luxury resources in particular, I'd say] need to come down. (I really like VEM's "no bonus Gold for river tiles until improved" rule change for this reason, among others.)