Ah, I get it you don't take the subway (or other crowded public transportations) too often...
Regarding the time needed for this, when I put my own card behind my phone, it really worked in roughly a single second. And it does work as fast through multiple layers of clothing as long as there's nothing metallic in the way. Now, in very crowded area, peoples get pushed on each others. If it was enough in the past for a skilled pickpocket to steal your wallet without you noticing, clearly it's enough promiscuity to do a contactless swipe over your pocket.
Now, the question of multiple NFC cards is real, but you assume that people who have multiple contactless cards hold them all in the same place. Unfortunately, for it to mitigate this "attack", all the card need to be on the same technology (for example, my transportation card doesn't talk NFC and don't seem to interfere with my phone NFC reading capabilities). And some people find it more convenient to "spread" their contactless card, so they can just push their wallet/handbag/whatever on the NFC reader instead of taking out the card itself. Again, convenience my very well be in the path of security.
So, all in all, yes, I have evidence that reading an NFC card through clothes can be done efficiently and go unnoticed. Also, since you mention tinfoil wallet time, for NFC it might be enough. I said it in another post, but a "simple" metallic card holder render my cards invisible as far as my phone NFC reader is concerned, so it might be a short term solution. But I also don't doubt that it's infaillible, as boosting the signal from the receiver side might be enough to get through that. YMMV.