Identity and abuse in software build around anonymity

I am developing a new application (web + mobile) that sort of builds around anonymity and requires a big audience to be interesting. People will be in direct contact with each other (one on one), but they wouldn't know anything about themselves initially. It might be seen as a sort of a game with outreach to real life and people.

Optimally, I would like to allow just anyone to use the app without any restrictions. Ask them a few basic information like what language they speak and where are they located and then let them roam. On the other hand, I want users of the app to be serious about its purpose and not to abuse it for their agenda/spam to annoy legitimate users. I don't know yet if it's gonna be a real issue or not.

Identity verification

Since the app builds around anonymity I find it sort of weird to ask people to register an account immediately. My goal is to allow them to keep using the same device anonymously. Later when they want to use more devices, they can register to persist the account.

Not to mention that any sort of registration with email or social providers is a hardly viable method of identification. For persistence purposes, it's enough.

Probably the closest to the person's identity today is a mobile phone. I can send one time SMS with code just to verify they own it and keep that phone number in some database and block access if anyone else tries to use the same number on a different device. Burner phones kinda make it difficult, but I like to think that not everyone is living in American spy movies :)

Here comes my first question. Is asking for a phone number considered part of bad user experience? Especially when it's sort of experimental kind of app. Could it drive potentially "good" people away? Of course, an explanation of reasons would be necessary, but that's probably hard to achieve in some unobtrusive way.

Identity by payment

The app generally won't be free. I am not decided on the specific monetization model yet. Ideas are mainly between onetime fee or credit-like based to spend with usage.

Either way, paying for something does feel like it establishes a sort of person's identity. I don't mean credit card number, that's probably too easy to get another one (less easy than email or FB account). I like to think if a user decides to pay, they want to use the app for real. Of course, some people might find the app as a good platform for their kind of agenda and pay too, so it's far from the ultimate solution.

However, the problem of paying before being able to try the service could be motivation to never try it out. That especially applies to onetime payments. It would require a clearly defined money-back guarantee for a limited time. With the credit-like solution, it's probably better if they can get money from the wallet back.

Another problem is that I would require credit card payment and would have to opt-out from modern methods like PayPal, BitCoin, PaySafeCard and similar as they are too easy to duplicate. That alone is a weird aspect considering the focus on the anonymity of the app.

So the next question. Could be asking for payment immediately considered better than asking for a mobile phone number?

Combination of both?

In conclusion, both methods might have an apparent impact on conversions and either is bullet-proof. Would it make any sense to allow the user to pick the preferred method? I mean they will have to pay at some point anyway, but if I can verify them with phone numbers and declare some sort of person's identity, I can then provide some free trial before they have to pay. Could such an approach prove helpful?