Any format gets solved. The speed with which it gets solved by players is independent of whether or not the format contains broken cards.
This is the part I don't agree with.
Standard is a rotating format. Its current power level dictates the power level of cards that will enter the format from a new release. R&D pitches cards at roughly this power level, and tries for a diverse environment where there is no clear best deck. So everybody who's interested in Standard can find a competitive deck suited to their playstyle. If the power level of the new cards is too low, there will not be enough change in the format to make it interesting. But if they push the envelope, sometimes a card ends up broken. Point being, the higher the number of powerful cards they design, the harder the format is to solve, and the possibility of a broken card slipping through increases.
I personally don't think they designed a broken (format-warping) card in the last few years. A few close misses, but nothing really broken. Standard seems quite healthy, with the best deck changing frequently. But I'm not a constructed player, so this is all second-hand wisdom. Maybe you have some candidates in mind?
You might argue that Rhino caused the Pod ban, but (even though I lost some money there) I agree that Pod was putting too many constraints on the design of new creatures, so the format is better off without it. And this seems to be the general philosophy: we develop for Standard, and fix any eternal problems with bannings. If you accept this, than their track record is perfect since JTMS.