Paypal (and subsequently Venmo) offers it. I've "instant transfered" money from eBay sales right to my account. They do charge a 1% fee (up to $25) versus zero fees for classic ACH transfer. If I need the money right away, I'll pay the 1% but I usually can wait the couple days.
In many cases they’ll be paying 1% of e.g. $40 either to avoid having to think about this any more or because they have extremely toothy consequences to not having the cash today. e.g. The implicit interest rate on an NSF fee if they don’t fund the $10 overdraft currently happening on their checking account due to the rent check being deposited, which they have 3 hours to cover before the cutoff, is on the order of 3.8e200%. ($35 interest to borrow $10 for a day.)
Venmo used to have a flat fee of $0.25 then they changed it to 1%. I'm guessing for most people, it would never be a problem since most people are usually only sending small amounts to eachother on Venmo (paying someone back for lunch or splitting utilities) but now Paypal gets a larger cut of people doing instant transfer of things like rent payments.
I had $2K in my Paypal account. I had about $1200 in my primary checking account. And another few Gs in savings.
I needed to pay a $2700 expense. I could have transfered from the savings, but you are restricted to the number of times per year you can do that, without penalty.
TLDR: I have no problem sacrificing $10 to get immediate access to another $2K in cash, with the thought co-resident in my mind that I do not want to incur any potential savings -> checking with-drawl penalties.
The APR in this case is meaningless to me completely. $10 for low latency access to my cash is a small price to pay, versus waiting a day or longer for slower (free) transfer methods to complete.
On the bank side, one of the main providers offering RTP payments to businesses right now is JPMorgan Chase. If you have a commercial account with them, you can originate RTP payments.