In our party, we had the tankiest abjuration wizard on the planet. They had plate armor that had on-attunement proficiency, and they had 20 Con and the Tough feat. Fun fact: Bigby's Hand uses the caster's HP :)

I've used this at the table quite a few times, honestly it's fine. You get it at level 18 as a single-class Abjuration wizard anyway, and the ward cap is low enough that you're rarely blocking more than one turn of damage - and there are a lot of ways to do that. A Rogue will often mitigate more total damage with Uncanny Dodge, for example. It becomes even less noteworthy in practice because so few tables are willing or able to run a full adventuring day - when you might only be getting one or two encounters per long rest, the ability to recharge up to 40 tHP between fights means a fifth or less of its theoretical peak value - and towards later levels, you may find yourself with so many superfluous spell slots that you could fill it up with higher level abjuration casts and not feel much of a loss. I'd argue that armour of shadows is still secondary to agonizing blast and pact magic as "things that make a 2 level Warlock dip nuts", even for abjuration wizards. And it may even be suboptimal to take it as a feat - any situation where you wouldn't take the Tough feat is a situation where you likely don't want to take Armour of Shadows as a feat, unless your DM very consistently does 4+ encounters, very consistently spaces those encounters out enough to fill up (so no straight back to back encounters or "responsive dungeons") and wouldn't be the type to throw more damage at you to offset the extra ward HP.

It's not that wild, cheesy, or overpowered. You don't get that many hitpoints out of the ward. Also Sage Advice says this works as intended.

I did this with the original EE material that gave deep gnomes nondetection at will. Admittedly, the eldritch invo to just grab mage armor does seem pretty useful to avoid a slot tax on wizards, although picking up lightly armored can achieve a similar buff

If allowed to use Mark of Warding Dwarf from Eberron, you can get Armor of Agathys as a wizard spell at level one. It's pretty powerful early game since so many enemies are melee.

At level 20 you can cast invulnerability to be immune to damage for 10 minutes. Replenishing 45tHP out of combat is not much in comparison to that. What's crazy though is involunerability is an abjuration spell, so it replenishes 18HP on your ward in combat ready when your 10 minutes are up.

It's not that many hit points. Honestly you could just ritual cast Alarm for the same effect. It's only broken once you get Spell Mastery at lv18 for infinite uses of Shield every turn (permanent +5 AC and +2 Arcane ward HP regenerate each round)

Had a player do something along these lines once, and yeah, they had maximum ward between fights. It honestly wasn't that OP compared to a lot of the shit I've seen in my own games.

Omg level 20 this is 45hp extra... you can destroy a city on level 20 and you think that will do something? Why peaple think about their build in level 20 when they will go about level 12 in most of the time

If the DM refuses to let you use this build, call the failed writer a legbeard. DMs aren't people so it's alright.