This is largely how I've operated for years with Google Voice: doing all of my SMS/MMS messaging and outbound calls (inbound, not so much) from the voice.google.com web app in my desktop browser.
If my life circumstances were a bit different, I could happily live without a phone and minutes+data plan. As it is, my wife would not approve...
My primary number has been a Google Voice number for a decade, and when I do use my actual phone for SMS/MMS and calls, I'm using the Voice app on there too.