Difficult to say without a thorough analysis. For one thing, the amount of minerals gained by buying the output of civilian mines can vary greatly per dollar spent, because the output purchases are at a flat rate per mining complex, while the actual mineral output that you get in return for your money depends on the number of mineral-types at that mining site, their concentrations, and your mining tech and governor +mining bonus.
That doesn't actually matter though. The output of one complex is the equivalent of 10 mines. It doesn't matter where you put it or what administrator is in charge, does it?
The question is: Does the cash output of 10 financial centers equal or exceed the cost of of buying the output from a single civilian mining complex?
Each civilian mining complex costs you 250 wealth per year if you buy the mineral output, while if you don't you can tax it 125 wealth per year... a difference of 375 wealth per year per complex. Remember that you must either buy or tax all of the complexes at any specific site as a single group... eg: if the civilian company has six mining complexes on Comet Halley, we can either tax all six for a total of +750 bucks per year or buy all six for a total of -1500 bucks per year, but we can't tax some and buy others. You can, of course, tax the mines on Comet Halley and buy the mines on Comet Encke.
So basically you lose opportunity costs - civilian complexes decide where they want to go on their own, but you have control yourself over where you put your pre-built mines.
Then again, what output you buy is also entirely your own choice, so in that sense it's not exactly that you lose anything.
But - if you tax a complex, you basically lose the minerals it produces. They go into the civilian sector and are never seen again.
edit: Oh, and let's not forget the cost of actually getting those mines to their destination. Especially if fuel is an issue ..
Each financial complex (and each million taxpayers) gives you 20 bucks per year. For example, Earth has 2,848.92 million people and provides 62,676 bucks in taxes. Discount my (governor's) +10% Wealth bonus, and that's 20 bucks per million dudes.
Why would you discount the governor bonus? That planetary governor would be there regardless of the financial centers, wouldn't he?
Nor would you discount the governor bonus if you were to put mines down yourselves. BUT .. you also get that bonus on civilian mines, don't you?
Nonetheless .. 20 spacebucks per financial center, makes 200 for 10 of them. Plus governor bonus. Still nowhere near that 370, but we haven't researched any economy boosts yet. Not sure how they stack, but +20% +20% +20% .. tends to add up.
Looking at my (older) aurora installation an automated mine costs 240 spacebucks, plus 120 duranium and 120 corundium. A financial center ALSO costs 240 spacebucks, plus 120 Corbomite and 120 Uridium.
So the costs are basically the same, and the minerals depend a tad on what kind of minerals you find a lot of.
We are currently spending 12.7% of our expense budget totaling -2,975 bucks per year on purchasing minerals from the civilian sector. Tax revenues on civilian shipping, colonists, exports, etc represents 3.1% of our income totaling +2,136 bucks per year. We have an annual budget surplus of +6,600 bucks per year, after all expenses including research, construction, ship building, purchasing civilian minerals, etc. We're currently sitting on half-a-million bucks in the bank.
So right now buying the output makes sense, and we don't need financial centers to support that. I fully agree on that.
However, considering the growth rate of the civilian sector, I know buying these minerals can add up to a rather substantial portion of your budget. So much so that at some point it really starts being worth considering whether the financial center isn't actually really the better thing to build - when your choice starts to boil down to: either tax the civilians (giving them the minerals they mine) and build automated mines, or build financial centers ..
That being said - economy research probably is even better in this regard
Don't get me wrong, I fully support the current policy. I just wonder what happens if the civilian sector's growth outstrips our population growth by a big margin.