It would be great if somehow it would be possible to show the account phone number for each contact (on their contact sheet). Is this possible somehow? Since entering the account phone number for each contact would seem a but redundant to me.
The best possible way to achieve this is using a Cross-object formula field. Since Account is a master of Contact, you can access Account fields in contact Formulas.
You can use this document to help writing the formula. There is a formula to display Accounts website on Contact, use it to display Account contact.
Do mark this answer as 'Solved' if it solves your problem.
Like what Sforce.Ninja suggested, your best bet would be using a cross-object formula field. There's a formula you can use to display the accounts' website on contact then use it to display the account contact. I think this documentation should help.