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That's a great question- unfortunately, Family Allowances isn't able to control anything on Wifi. T-Mobile does offer FamilyMode now that allows for more solid restrictions regarding data usage specifically.
Posts have already said FamilyMode can easily be disabled (both with and without notification).
And, if someone is interested in FamilyMode, I'd suggest buying the device from Circle directly because it doesn't have a monthly fee that way. After 10 months, it's cheaper that way.