I have run an all arcane caster campaign..... not by design but that is just how the classes shook out after character creation.
Based on my experience, the concept is doable, if the class mixes are right.
At low levels, the characters are vulnerable to being bulldozed by melee types unless they are careful.
At high level, the party can be hell on wheels. Once the party got about 13th level and up, they frequently would blast/obliterate the opposition to cinders in one round of combat.
All the characters had improved initiative and good Dex or Dex buffs, so frequently, the entire party would get initative and would slag the oppostion before the opposition could effectively react in a meaningful way.
The party would come up with spell combinations that were lethal, especially on the usually solitary BBEG. Some examples - one spell caster would take a ready action to cast wall of force or telekinetic sphere or crushing sphere. Then the other casters would cast spells like cloudkill, creeping doom, or any spell that dealt continuous damage for X rounds. So, the BBEG would get several duration damage spells cast upon him or in his square, then the readied telekinetic sphere / walll of force would gift wrap the BBEG so he couldn't escape the AoE of the spell effects.... Nasty
Of course, my players all liked playing spellcasters and were very good at that role. Once they gleaned onto doing party spell combinations, the bad guys had a tough time staying alive unless they had significant spell resistance or were constructs.