Well I don't use a lot of conjuration spells.Usually just the mob of the element I choose(fire usually so flame atronach) so he won't be taking damage from my spells.They tank good usually , and you can always pull back and heal yourself quick.However what if you are fighting multiple ranged enemies at once?Like 2 archers and 1 mage , if you get a hit from all of them(on adept) you are nearly dead(and on master you are dead).In that kind of situations shouts won't help since the range of wuld/fusroda may not overcome their range.About the warrior part(frost slows them to hell) you can end up fighting darug overlords(hwo shout) or any other shouter , how can disable you for long enaugh to finnish you up.
Besides all that , you have your greater 2 enemies-Dragons and Assassins.Dragons will be able to finnish your mob fast , then he goes for you(also he has AoE damage so you will end up taking some pain).Assassins are very rare in the game , and warriors tend to not give a damn about them since they will tickle them.But well planed sneak attack can end you because it will catch you without your mage armor on.Even if you fight face to face some sort of guy like that, he usually evades your porjectiles and gets to stab you.
I did not plan to make a battle mage , a battle mage uses a one handed weapon or something like that along with the spells.There is one last reason of why you should get health&armor and it's for later in the game when you get your destruction/ilusion or even restoration to master.You must move inside a pile of enemies and drop those spells that take about 5 precious questions to cast.
There's lots of tactics to use, situationally with a Pure Mage. Just to run down the ones you mentioned: Say you're taking on the Foresworn, which usually have a bit of Mages, and Archers on to of their Dual Wielders. Assuming you can Evade, or have already dealt with the Meleers, first Wuld within range (archers always have a bit more than mages) and stunlock the Mage/Archers with Impact, so they can't fire/shoot back.
With Flame Atronach, the thing is that's not a very good tank, but another Glass Cannon. It skates around, throwing Firebolts, but if it is mobbed, and killed, it often takes out the ones around it with it's death throes. Be prepared to mop up any survivors, and recast. I play on Adpet, Master if to compensate for OP builds, which a Glass Cannon is not. If you're good with them, you don't need to dial up the difficulty to the point where you're getting 1shotted.
The only thing I get Snak Attacked by regularly is Sabercats. So, if I'm in their country, I keep Ebony Flesh up (you can recast before it wears off) and Detect Life for early warning. Also, Flame Cloak, and/or Wall of Flames help finish them quickly. Ok, not the classic 3rd era Battlemage Class, but still a Mage/Warrior hybrid, because you're using Warrior Skills.
I assume you mean Master Spells, which take 3 seconds to cast, while you're rooted to the spot, can't do anything else, and can be interrupted with a Stagger? I don't use them, they're suicidal with a Glass Cannon, because you Have to surround yourself (Except Lightning Storm, which will likely get you shot) and they make you too vulnerable. Try Ice Storm, and Frenzy, or Flaming familiar. There's a lot of other good combos, but these prevent you from Dual Casting, which increases your Magicka Drain a lot more than your Damage.
Throw an Ice Storm, and chase it with a Flaming Familiar in it's path (or cast them together.) This actually kills, and detonates it, but anything in the AOE is now Slowed, and on fire. It takes a bit of practice to time it at different ranges, and to account for movement, but this is extremely powerful for large numbers, and doesn't cost all that much Magicka. Also, you can use this combo behind cover, since the summon runs around it, while the Storm goes right through, but Aura Whisper really helps for aiming/timing.
Frenzy is better than Mayhem, because you can start a Moshpit over there, while maintaining the mobility to stay out of it. Cast them atlernating hands to carpet bomb large numbers, such as Karthspire. This clumps them up firghting each other so you can blast them with AoE Adept Destruction, or hose them down with Wall Spells. These are great, because they do up to 75 damage for 20 seconds, as long as they stay in the AoE. You can even Impact Stun them so they don't run out, (as long as it's not Stormwall.)