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SgtSurehand Aurora store is insecure because its secure connection and signature verification are less hardened than Googles Play Store. Attempting to use it with your own account makes you look like a bot and Google might suspend your account for spam.
This is why GOS doesn't recommend it.
Specifically, metadata verification is not done, its been known to grab wrong app versions, and no certificate pinning.
People don't criticize obtainium because obtainium only attempts to pull apk files from github, its security is sort of already apparent. The Google Play Store is trying to do something completely different in terms of security.
Your analogy on "checking if the item you bought was really from the store" is a fundamental misunderstanding of how network security functions.