It isn't really not paying fee. Technically it is Xapo which is paying the fee for you. Coins.ph ( a local exchange) also have the same feature where they are the ones paying for your transaction fee. Tho it always isn't a very good option nowadays because they are paying the minimum which I think is around 10k to 25k satoshi which sometimes isn't enough to get your confirmation confirm as fast as you want.
We must understand that even with these fees getting paid for us by Xapo or Coin.ph or even if other wallets start doing so the transactions will not arrive faster, in the transaction core code there is a default value to fees that go to miners which you can modify them, and all that those wallets are doing are paying this default value and if you want to make the transaction faster you are going have to manually change the fee value so it becomes priorities.
Less than 0.001 takes more than 1 hour, and 0.01 or large amounts takes less time. I got transferred within 30 minutes with 2 confirmation.
The transaction should arrive instantaneously, if the transaction is valid and has the minimum relay fee. Ideally, the wallets can implement a system which has dynamic fee and the fees will be adjusted according to the user's needs and network. Some of those "wallets" sends transactions in batches so as to save on fees.
The total fee doesn't matter, fee/size does.
On a positive notes, what will happen when more than 50% of bitcoin users will be adopting Xapo wallets ?
Because Xapo to Xapo payments are instant and email based. It means it will never touch blockchain but your Bitcoins will be credited in your account.
To get rid of greedy miners, we may need to centralize bitcoin under Xapo. This is the result if we start using Xapo wallets in large numbers.
Likely not. But if it does, the users will have their coins under Xapo's control. The transaction volume would reduce if the transactions are done offchain.