>Would you say the same about your phone number?

No.

>If not, why?

Because a phone is a universal method of communication, for businesses, spouses, families, friends, and everything in between.

Twitter is yet another social media gossip discussion site, just one with a gimmick (limited characters).

>If I run my business on Twitter (or YouTube, or Facebook) is it that different from a bank?

The only businesses run on Twitter are ads, influencers, and PR -- and those deserve to die anyway.