It's been done. For example, app.net. https://en.wikipedia.org/wiki/App.net I deleted my Twitter account and joined ADN. But not many followed that example. Most people stuck with Twitter, ADN never reached "critical mass", and it eventually shut down.
I don't think this is a technological problem. You could say it's a marketing problem. The critical mass is essential to a social network. ADN didn't get it. Mastodon hasn't got it. Twitter has it, Facebook has it, and it's just hard to compete with that.