Twitter has massive data on your interests but collects only minimal information about you vs, say, Facebook which has your name, birthday etc etc. I would also argue that Twitter has BETTER interest data than Facebook b/c you are constantly interacting with thousands of tweets a day across multiple dimensions. Facebook tends to be your family and a couple pages you happened to like.
If they get your phone number, they get all of the available "data in the cloud" about you e.g. income, purchasing preferences etc. Cross reference the interests with that cloud data and you have a very precise target profile to sell to advertisers.
Some VoIP providers do a PAYG model, so you can choose from any number of phone numbers, regional, local landlines or from mobile numbers for free and only pay when you make a call or answer their answerphone.
Now obviously Twitter will send text messages so you never incur a cost from the VoIP provider.
So how does a phone number solve bot activity?
I don't know how the implementation works, if theres a way to check for virtual vs. real number, but some sms verification service provider seems to have successfully implemented a filter on Google Voice
Makes no sense. If they wanted to require a phone number to keep out bots, they would simply ask for a phone number at registration. Delaying it like this, claiming “suspicious activity” is hard to see any other way than how I described it.