Not only platinum, but also with fool's gold. Opening Mint/Fool's Gold is huge.
But the 5/2 vs. 3/4 randomness doesn't bother me much. I know it's random, but it's upfront and done with. I don't play for ranking, so I just approach such a game as one where I started at a handicap and ought to have fun trying to make do. I don't feel like the game is waste. Much worse is when there is beautiful support for lining about a nice Minting hand, and you chase it for a dozen turns before it pays off -- those games are full of regrets, even if later analysis suggests that it was wise to have gone for Mint over, say, opening Forager. In fact, these game are much worse in my mind than ones where your opponent lucks out with Mint.
I think what irks people about swinginess re: Mint, Treasure Map, or Tournament is that sometimes you'll build towards that ideal hand, but all the planning in the world fails you, while your opponent just stumbles upon it by chance.
Now, people sometimes complain about the noob who buys Treasure Map T2 and T3 and gets his pairing on T5 without any supporting cards. But at least that player took the risk of buying the Treasure Maps. With Mint, you may have no intention of chasing it, but then you draw CCCCC, or CCCC-Smithy into CCCCCCC. OK, I've never actually witnessed the latter, but my point is that Mint swinginess is often a deus ex machina on a board where no reasonable player would have intentionally pursued it.
But ultimately, the irking doesn't bother me much. I'm fine with some swinginess. Like Donald has said, a bit of randomness lets you relax. I don't want to be wondering if my opponent if already planning out the next 5 turns while I'm only looking ahead 3 turns. I like the attitude of crafting some grand strategy, keep a bag of tactics in mind for executing the strategy, and weighing the risk at each decision.