The status quo rails in the U.S. are ACH or Fedwire. These are slow and require you to get connected to the rail in some way (directly or indirectly). And they have fees.
There is also same-day ACH and the new FedNow. Which are faster, but still require some kind of connectivity and have fees.
The cost of stablecoin settlement is mostly the gas fees of the chosen chain. There are various optimizations possible such as private chains and off-chain ledgers (no gas) and some single on-chain settlement to minimize gas fees. Note that these type of stablecoins are closed-loop and are not publicly available.
As I said in my other post, these institutional stablecoins are mostly just MVP use cases until regulations are finalized. Depending on the final regulations, there are quite a few other possibilities.
Source, I work for a large financial institution and run a team that launched a stablecoin this year.