I disagree that private companies are free to regulate speech on their platforms. Companies which are in the business of carrying communication may not censor that communication. Just as the phone company can't disconnect your service because of what you say to someone else on the phone, companies like Twitter should not be able to shut down your service because you say something that they don't like. When you speak on Twitter you are not speaking for the company.

No one should be able to tell the companies what to say or what not to say when speaking as the company or when their management or employees are speaking.

Your comparison to speech in your home is incorrect. A better analogy is to speech within a public square, shopping mall, etc. Twitter, Facebook and similar platforms are the modern day equivalent of the public square. Limiting speech in the public square has long been unconstitutional. This protection was extended to shopping malls and similar premises in the 70's based on them becoming the equivalent of the public square. That function has now moved online in much the same way that shopping has moved online.