Smart phone mapping is excellent and much more convenient and feature rich than paper maps or even most hand held GPS units.  There is really no reason not to use them,  barring the cost of the phone and that subscriptions are required for some features.

The down sides include:

  1. Phones require charging and battery life can be fickle.
  2. Phones are fragile and break easily.  They can just stop working.
  3. Phones can be easily dropped and lost
  4. Phones don't work well below freezing
  5. Phone screens are small and good printed map are much better at providing instant overview and detail.

While these things can be mitigated or avoided to some degree it is still generally wise to carry a printed map of the area through which you are traveling along with some sort of decent quality magnetic compass so you can get a reliable direction. 

Failing that, at least some sort of backup GPS device so you are not relying solely on your phone. If you are traveling in a group then that backup can be other peoples phones.  Just make sure that at least one other in your party is also setup to use mapping on their phone in some way and has local maps cached...There are free solutions which make a rudimentary backup that everyone should have.

If you will be following trails in a reasonably popular area during the popular season then the importance of a carrying a backup is obviously diminished.  Unnecessary redundancy can be inhibiting if it requires any effort so obviously once can apply some judgement.