[RPG] Is the Moderately Armored Feat really the only way for the dwarf to get shield proficiency without multiclassing

I really enjoy working out rather unusual character builds, or taking a subpar character concept and try to make it work using min/maxing, point buy and having every level from one to twenty planned out before even starting the adventure (ability increases, feats, equipment, etc). My latest project is a wizard that is as tanky as possible (tanky meaning having high AC in this case).

To achieve this, my wizard would be a mountain dwarf (starting with light and medium armor proficiency), and have 14 Strength. Depending on how the campaign goes, around the time I'm getting close to having enough gold to buy a suit of plate armor I would forego an ability score increase in favour of the "Heavily Armored" feat (also giving me +1 Strength, raising that ability to the score needed to wear plate armor without getting a movement penalty.

Now, I would have an AC of 18, which is quite high for a wizard. But, as stated, my goal is for my character's AC to be as high as possible. Adding a shield to my character's equipment would seem like a cheap way to get an extra +2 AC for an impressive total of 20. But this is where I finally get close to my question.

Shields have a separate proficiency in 5E and wearing armor you are not proficient with not only imposes disadvantage on any ability check, saving throw, ar attack roll that involves Strength or Dexterity, but also makes it impossible to cast spells. Not being able to cast spells would make my wizard kind of pointless so in order to make this work I would somehow have to get proficiency with shields.

At this point there are two ways to get shield proficiency in 5E: multiclassing one level in a class that has shield proficiency or taking the "Moderately Armored" feat. Multiclassing isn't really an option for me since it would leave me unable to get the high level Wizard features. So I would have to take the feat just to get shield proficiency. Since I'm already proficient with medium armor this seems like a complete waste of a feat to me. If that is as it is intended to work I wouldn't take the feat.

So my question is: Is the Moderately Armored feat really the only way to get shield proficiency without multiclassing?

Because it sort of seems like an oversight. Now, the developers can't reasonably be expected to take in to account people like me creating stupidly specific situations like this: a heavily armored dwarf wizard who uses a shield (my character would still be able to perform the somatic components for spells even wielding a shield since he would not wield a weapon). For the vast majority of character builds this would never be an issue, but I really think shield proficiency should also be included in the "Heavily Armored" feat.

In my other wacky character concepts I have found that sticking to the rulebooks generally works out just fine. My DM also sticks to RAW and doesn't use any homebrew rules. Normally I'm all for sticking to RAW but this just seems kind of silly. According to the rulebook, my wizard could hold a chair in his left hand and would still be able to cast spells, but when he's holding a shield this is suddenly no longer possible.