I just wish banks had the option to get a card without a magstripe. I could use the chip-only card for day to day stuff and only use the magstripe when I travel to the U.S.

You can easily demagnetise it, with even a kitchen magnet [0].

[0] http://lifehacker.com/5780617/how-to-prevent-yourself-from-o...

Yes

And then your card is useless when in a place that only reads the stripe (like, that uses Square)

The European competitor to Square uses the chip. And I already suggested to keep a separate magstrip card for traveling to less developed countries.

kalleboo was asking about getting a card with no magstripe, so I assume he's OK with that

You can clone a "magnetic card" from a chip card - it's magnetic stripe will be identical, but you won't have the private key of the chip.

And afterwards, if the bank knows that it is supposed to be a chip-capable card; and the location (country) is supposed to be chip-capable, then all mag-stripe transactions are rejected even if the "all required information" is correct.

The banks could do this, but in general they don't seem to - it's too annoying for their customers when the chip is covered in dirt, a bit damaged, whatever.

Good point, I hadn't thought of that. I suppose I should call my bank and ask them. But how do I know what they're saying is true? Usually when you call support (never tried calling a bank) you get some blonde that tells you nothing except that "everything is secure!"...

On the other hand, the card doesn't slide all the way in anymore. Just far enough so that it sticks and it can read the contacts, so at least they can't grab all the information on it.