On principle, I believe if the employer isn't paying for my phone, they don't get to expect the benefit of it. If you need to contact me, pay for a phone for that purpose and I'll carry it when I'm being paid to do so.
In reality, however - it's just something you have to look at in terms of total compensation for the job. Are you happy with what you're being paid to do what is being asked? As you mentioned in the OP, once customers have your personal number, you're on call 24/7. If you're not being paid enough to compensate for that expectation, that's something to discuss with your employer.
Personally, I'm on call 24 hours a day during alternating weeks. Work provides me with a phone which I forward to my personal device so I don't have to carry two phones around all the time. If I'm going on vacation, I kill the forwarding function and let work calls go to the work voicemail.