I can't see the banks being happy about customers cloning their own cards. In fact, it will probably be a convenient excuse for them to absolve themselves of all liability in the case of loss, theft, or misuse. Some, if they found out, might pitch a fit and close the account.
This also is going to pose a lot of problems when used with non-domestic cards, as they point out in their FAQ. It's possible to use an EMV-based card with just the magstripe, but it's a pain in the butt and the bank may well be aware that all your meatspace transactions are not using the EMV-chip. They may assume that your card is broken or (quite correctly) cloned and block it. A call from the fraud department may well lead to a fit being pitched.
From wikipedia: "Magnetic stripe cloning can be detected by the implementation of magnetic card reader heads and firmware that can read a signature of magnetic noise permanently embedded in all magnetic stripes during the card production process." [0] Oops, now your card is blocked.
Retailers might also get skittish if they figure out this isn't actual bank-issued plastic. They may well refuse it because of the risk of fraud. I would. I really wouldn't want to be running someone's cloned card, even if the cardholder was the one that did the cloning. In fact, it might jeopardize a retailer's merchant account if the acquiring bank found out the merchant were running cloned cards!
The best way to counter a bulky wallet is to not add bulk in the first place. How many credit cards and debit cards does one need to carry on a daily basis? I carry maybe two or three cards, some ID, my Oyster card, and a Costa rewards card that I use daily. I also have a backup wallet that contains a second set of cards in case I lose the first. The bulk of my wallet is receipts that accumulate, but even when I carried way more my life wasn't burdened by a whalelike wallet.
It'd also be a pain in the butt to use this with some rewards cards. For example, my Costa rewards card is swiped at the same time as I'm paying. Would I really want to fumble through pressing a button to find the right rewards card, give that to the cashier, have it handed back so I can fumble through pressing buttons again so I can pay? Certainly not, and even less so the impatient people in line behind me.
Sorry to promulgate the Hater News stereotype, but it's just too easy to poke holes in this idea. It has superficial appeal but I really wouldn't pay $100 for so many potential problems, especially as it would only make my wallet a few mm thinner.