You provided this method of communication. You gave him your phone number. You are responsible for this method of communication. If your phone is broken, it's your fault. Nobody else can change that.
That said, phone calls are not a good way to communicate asynchronous messages. You cannot send a document by phone call and calls are mostly inconvenient. The chances of actually calling when the other one has nothing better to do are slim. So preferring email is normal. But it is your responsibility to make that clear. Don't provide a broken line of communication in the first place.
A personal note: I'm working in IT. When a candidate has a broken phone and does not give me a replacement number, that would be a big red flag. How is he to handle the tasks I assign, if he cannot find a way to fix his own phone? Even if it means sending it in for service. But just leaving it broken would have me thinking about his ability to do the job.
So next time, state clearly that you want email communication. If you need a phone number, provide one that works. You are under no obligation to pick it up whenever someone calls, you are not a call-center. But it should be working. Preferably with a way to leave a message should you not pick up, so you can return the call.