One issue that has not been mentioned is administrative matters.
Usually when you start as a grad student, your department asks you to fill out a form with contact information, typically including a phone number. (You may have a similar form for higher echelons of the university.) If you put a phone number on that form, the department's administrative staff is going to expect that calling that number will reach you. The vast majority of administrative matters are handled by email, but occasionally there can arise something urgent where someone needs to speak with you right away. ("We need this form signed today or your stipend will not be paid." "Another TA is sick, can you take over her class in 15 minutes?" "Your office is being flooded with sewage.") In those cases, they may very well try to phone you - and it's not so good if this results in them leaving a message you will never hear.
And if you don't put a phone number, it's likely that you will have to explain why you don't want to be called, and hope that your department's staff are understanding and willing to be flexible. Note that administrative staff members tend to conduct much more of their daily business by telephone than academic personnel, and may find it much less convenient to try to reach you by text message, instant message, etc - so keep in mind that your preference is having an impact on other people.
If your friend's reasons for avoiding phone contact are reasonably compelling (hearing impairment, stalkers, etc) then I would expect that accommodations can be made. But if they are frivolous or appear to be personal eccentricity, this may lead to friction with the administrative staff. (And that's not good, they have a lot more power than you may realize.)
I would actually expect this type of contact to be a bigger issue than with your advisor (who is probably fine with contacting you via other means) or your students (who should not get your personal phone number anyway).