Nothing.
Its clear you still don't get the concept, and that is understandable, as I only understood it when I started to use it (and now I will not use anything else).
When you open a transferwise account, you can choose to create an 'account' for any currency of any supported countries, in your Transferwise dashboard.
So, for example, if you want to keep USD, you open a USD balance, and you then get a US account (in your transferwise dashboard) with US bank info that you furnish to people in the US. They simply pay into that account. To them, its a local transaction with all of the numbers/forward accounts/etc etc specific to their country. When they pay into that account, you then get a US balance in the USD part of your account in your Transferwise dashboard. You can then choose to keep it like that, or convert it to CHF. When you 'send' it to your CHF balance, you get the closest FX rates to what you see on the internet, and your USD balance becomes a CHF balance. It might cost a few dollars, but is much cheaper than wiring/paypal etc. You can then chose to withdraw it to your local CH account, via IBAN.
Throughout this whole process, no money crosses any borders. Its simply marvelous.
👍
Edit : and it works both ways. So if you want to pay someone abroad, in their currency, with the cheapest rates, you set up a Transferwise transfer in their currency to their bank in their country ... after setting the transfer up with Transferwise, they will furnish you with a local account and the exact amount (in your currency) and reference for your transaction, that you then transfer locally to a local bank, and two days later the amount appears where it should be abroad in the desired recipients account. No money crossing no borders.