As I understand it, this was the premise of cable TV - pay for your cable, and in return you get no ads. Yet, here we are with ads on cable, because it turned out to be more profitable to both charge and show ads than just do one or the other.
No, that was never the case, it seems to be a myth that started getting repeated a lot in the last decade; at least, I've never heard of it before it started getting used as a “historical precedent” in discussing online advertising trends, despite is ahistoricity.
What you originally paid for with cable was access to channels, largely existing broadcast channels: not everyone was choose enough to the transmitter to get good (or even usable) broadcast reception, even when they were nominally in the media market.
From very early on, IIRC, the were (ad-supported) cable-only channels for which cable was the only means of access. Over time those became the main thing you paid for cable for.
Commercial-free premium channels were a later development, which you paid for (and still do) on top of cable (though they may be bundled into higher tiers). But commercial free service was never the key value proposition of cable.