Player's Handbook, page 6:
"Because there is so much diversity among the worlds of D&D, you should check with your DM about any house rules that will affect your play of the game. Ultimately, the Dungeon Master is the authority on the campaign and its setting..."
And the
Dungeon Master's Guide page 5, the introduction to Part 3.
There's no hard rule that a shield can be used as an improvised weapon, that you do not need to remove the shield from your arm, or that you can continue to use the shield as a shield while doing the above. RAW, while a shield is strapped to your wrist, you're not wielding it in one or two hands, the requirement of an improvised weapon on page 147 of the PHB. So it needs to be in your hands. Allowing it to be used while still strapped to your arm and out of your hands is a DM call.
In an unofficial response (on Twitter), one of the designers gave their opinion that you can use a shield as an improvised weapon and that you do not need to remove the shield to do so. They didn't weigh in on if it still functions as a shield. However, a Twitter response is not an actual rule, and even if it made it into a Sage Advice article on the website, that wouldn't overrule a DM.
Now, is it a broken combination? Not really, even if you allow the shield to still be used as a shield. It's a minor increase to Damage Per Round (<2 DPR since it's less accurate) and increases AC by 1. However, in place of taking the feat, the human could have taken a stat boost to Str or Dex, increasing damage by 1 and accuracy by 5% (15% more accurate with primary attacks compared to the shield) OR increased AC by 1 and Dexterity saves and skill checks. So it's arguably comparable. I'd be willing to allow it as a DM.