Right now it is not possible to compete with fast fiat transfers (e.g. card-to-card payments)
At least, on a consistent basis. But Bitcoin is very robust in this respect. There are ways which could be implemented to make transactions as fast as the network itself is (basically at speed of light plus communication devices delays), and that would beat the fastest fiat transfers hands down, which are still heavily centralized and require a few days for final settlements. Apart from that, with fiat transfers you don't know it either how long a transfer would take, e.g. international wire transfers may take up to a few days.
If you're purely focusing on IWT then it's obvious that they will fail to compete with Bitcoin, but that's not really the case with (yup, centralized) payment services that allow you to instantly transact with each other within their eco system. PayPal for example is doing quite a decent job in that regard. If you are looking to transact with your relatives or when you buy/sell something, where you use your PayPal balance as starting point, then it basically delivers you exactly everything you want (e.g. instant payments, security, etc)
But I don't in any way challenge that
And which I specifically emphasized in the first sentence of my post that you quoted. On the other hand, I used PayPal a few times in the past to move the funds from my PayPal account to my bank account, and it did take over a day or two (I don't remember exactly but the transactions were not instant by any means). Basically, banks are using their client money for some time earning profits, i.e. they don't credit the account as soon as they receive the money. This is a well known issue (or feature, from a bank's point of view). But that's not my point. Even with card-to-card transfers (which I use pretty often), you are still not guaranteed to receive the money immediately. Sometimes the transfers are pretty close to instant, sometimes it may actually take hours (obviously, banks are withholding your money for their own purposes). With Bitcoin offchain transactions (e.g. via exchange codes aka vouchers), the coins are transferred momentarily since there is no third party interested in keeping your coins