I have a 500 Mbps connection with a 1TB data cap, both pretty standard numbers in the US. If I used the connection at its advertised speeds, I would exhaust my monthly limit in about 4 hours. So no, that relationship is non-existent. The data cap math instead is "99% of our users use < 1TB, so we will charge the rest more because we can".
Or more accurately, to disincentive excessive use. They don’t need a cap to simply charge you more money, they’ve been doing that just fine with or without caps.
