Just looked at the terms of service you agree to in order to get this key.
I can see the low call limit:
You are limited to one hundred thousand (100,000) calls to the Steam Web API per day.
But also on the same page:
You agree to keep your Steam Web API key confidential, and not to share it with any third party. This license is personal to you and specific to your Application. You agree that you will be personally responsible for the use of your Steam Web API key.
TSA is a third party, so in order to get this badge, you have to break the ToS.
Source:
https://steamcommunity.com/dev/apiterms