SMS is sent by interfacing with your phone’s modem which is connected to the mobile phone network. How would a desktop app be able to do that, except for that tiny minority of users who have a computer that can take a SIM card directly for connectivity?

https://messages.google.com/ manages to do it by routing the SMS through your phone.

The phone app could sync with the desktop app. You type an sms to the desktop, it syncs with the mobile app, mobile phone sends the sms, gets the reply, and the reply is synced to the desktop app.

This would require your phone to be connected to the internet at the moment you press Enter on the desktop, otherwise it could be hours until the SMS goes out. For those on prepaid plans, it would also require that you have enough credit on that phone to send SMS. Perhaps the developers felt that there were too many uncertainties to implement this feature; users might have reacted negatively if it didn’t work for them.

Plus, Signal plans to eventually allow multiple phones to be connected to one’s account. Then, the question becomes: if you sent a SMS from your desktop, which of those phones sends the SMS and gets billed by the mobile provider for doing so? You might say that a setting could be made for that, but any new setting requires changes to the UI, too.

It works like this on messages.google.com as well. It's not a deal breaker.

By talking with the app on your phone and asking it to do it.