Sure, but you see all you did was convert stuff into other stuff - you didn't really do anything with it just yet.
If you need more Science and you can already build a Laboratory, it's good to build the Lab. If you need Culture and you can build an Alien Preserve, then you do that. The thing is, you can't always do that, and you don't always want to. Well, not with the Science and Culture - it's nearly always handy to have more of those.
If what you want is fast production of Battlesuits, you need to have the tech first. Until you have the tech, you have hammers that you have to spend every turn. You can't store hammers. Hammer-creating buildings and improvements are the only thing that allows you to "store" hammers, and they're not very efficient at that, of course. But then, if you want storage efficiency, you'd be making Energy, not Hammers.
+20% Affinity from Tech is surely a powerful victory aid, but before it comes +50% XP to Military units. Do I want that? Can I use that? If I never expect to wage a serious war (or I don't expect to lose to the AI in any case), then the first Virtue is completely useless is it not? It doesn't merely not pay for itself - it is completely useless other than a requirement for the good things.
Will Free Affinity +40% Intrigue, and Eudamonia - will they give me something like 500 more bpt? I'm kind of doubting it, but feel free to elaborate the cost/benefit calculations.
Point being, it's not culture spent that you should be comparing the Virtue towards. It's what the other thing that you got could be doing. Now, I'm not a die-hard fan of the Knowledge tree, but the +0.25 science per person is pretty spiffy. The +0.25 Culture comes fairly early, too, and helps to expand borders neatly. Will I get that benefit from Prosperity? No. So I can't spend it on Prosperity and get a better thing that does exactly the same thing - perhaps I can get more value. That goes to balancing the Virtues against each other. But it won't be the same thing.
By the by, Recycler adds an explicit +1 hammer per Trade Route over and above its base effect, so if the Capital has 5 TRs coming in, the Recycler is actually outputting 7 hammers per turn, at least.