I don't think removing the phone on a permanent basis is the solution to anything because the fact is that they are a part of normal, everyday life these days. However I would remove temporarily as a part of consequences for bad behaviour, on the basis that it can easily be earned back with good behaviour. It doesn't have to be the phone, the approach applies to anything the child values - certain trainers/clothes, games consoles etc. If you're trying to set boundaries and teach the concept that actions have consequences, this is the easiest and usually most effective way to do it.
Example: child is rude. You don't scream and shout, you are calm. You explain what the child has done wrong and you remove phone. Explain what's going to happen. Insist upon good behaviour and the completion of household chores, maybe emptying the dishwasher. Child behaves and does their jobs, phone is returned. You can set timescales of perhaps three days. If child doesn't comply and bad behaviour continues, phone is not returned and you then remove something else child values. Carry on until child realises there's no benefit to them in misbehaving.
Of course it wouldn't be a one time thing. You will have to rinse and repeat regularly until child grasps that you are serious, and maybe extend the punishment time with continued infringements, from three days to four, five etc.
Similarly, go out of your way to praise and reward good behaviour.
I'm not a good parent. I have a temper which I work really hard at controlling because having to deal with my own temper upsets me, never mind the target of it. However I am a much better dog parent than child parent so I've got into the habit of using dog training on my children. Many people seem to desperately disapprove of this and think I'm nuts, but my children are actually very well behaved. I don't say it to boast because it definitely surprises me - sometimes I wonder if they're even mine or have been switched at birth!
I certainly wasn't that well behaved but looking back at our house growing up, there was no consistency or pattern to rules or punishments. I never knew what was fair and unfair or how my parents would react to certain behaviours. I felt very insecure and didn't really trust my parents because of it. I've been determined to do it differently with my own and while I do fuck up on occasion, I'm very clear on discipline and my husband has learned we have to be consistent on it - I used to have to regularly remind him that we never threaten things we're not prepared to follow through on. In terms of removing privileges he had a habit of saying things like "...or we'll cancel your birthday party!". To me this wouldn't work because we've paid for the bloody thing and invited everyone, so there's no way I'm cancelling it! But to threaten and then not follow through damages the process, so we make sure now that if we threaten a consequence, we absolutely follow through with it. Again, the consequences have to be reasonable, proportionate and actionable.
I don't mean to make it sound like our children live in a boot camp but I think they feel secure knowing the 'rules' and the system. These days with my eldest I very rarely have to threaten anything. If she starts pushing the boundaries I can usually just give a very stern look and she knows what's coming and that compliance is what's best for her! Ultimately children, like the rest of us, are self-serving creatures and while they do want to explore boundaries, they also want their privileges and in most cases will do what they need to make sure they get them.