Phone verification is a cheap way to mitigate the abuse, IMO. It also still has the possibility of being abused, you know in some countries, any individual is able to get/have multiples phone numbers.

As a reference for suggestion, I might take LBRY example to mitigate the rewards abuser. To be eligible to get a reward, new users should verify either using CC or phone numbers. In some cases, both of the options also get rejected if ever the user country is known to be a high-risk abuser. The solution for those rejected countries or an alternative way for users who want to preserve their privacy is to do manual verification. you can take a look at this to see more about it.

Anyway, as you can see in the above post, adding more information for the signup process will be good, we don't know what countries phone numbers are being accepted and how to format correctly the country code on the form. Also, wouldn't it be better to add some ToS and/or privacy policy about it?