Will they go away? No. Will they change? Yes.
We have already seen embossed numbers replaced with mag stripes, replaced with chip, and now replaced with tap. Yet, the card still persists.
It is easy to add new high-tech gizmos. The hard part is taking away the old, proven technology. Cards still have numbers because it is the only practical way to place a phone order. They have mag-strips because "everyone" can read a strip so it makes a great fall-back plan. And, swipe technology will stick around for quite a while because it is frequently used for low-risk, price sensitive use cases, such as in-store credit, loyalty cards, etc.
You are starting to see stripes being refused unless insert fails three times in a row, and the rules will get more stringent over time. But bottom line is that the retailers want fallback options because if you can not make your card work, they lose the sale and have to pay someone to reshelve your order.
The only thing I have seen disappear is the digits being raised. This probably has more to do with cost than anything else. Embossed cards are more expensive to make, and in-store imprinters have all but disappeared because they create a paper paper charge slip that is expensive to process.
