The problem with magstripes is I'm fairly sure there are some skimmers which basically read the card number off the mag-stripe when you insert it for a chip and pin transaction.
Because my card has been skimmed twice. The first time we were 100% it was a major retailer who was insisting my wife needed to swipe the card for a particular discount, but the second time the only in-person use we could remember was at a service station where we inserted the card to pay and pretty much the whole card goes in the slot.
You can read the magstripe from as little as about 1/3rd of the strip...though it's also possible someone is just embedding a scanner element to optically grab numbers nowadays, the tech is certainly cheap enough.
The trouble is it's really hard to reliably demagnetize a credit card, and the magstripe-less card rollout is being done incredibly slowly.
Newer cards don't have embossed numbers on the front anymore, only on the back, and these days I put electrical tape over them just in case someone is watching cameras. But I can't delete the magstripe and be sure it's gone reliably.