No they didn't, I've had phone plans with enough data to use WhatsApp 24/7 (around 2011 probably) way before unlimited texts (don't know because I haven't used SMS since forever). In fact I remember way back in 2008 using a website from my phone to send SMS instead of sending them from the phone because it was cheaper. Heck, I think I got unlimited data for WhatsApp before I got unlimited texts, and in fact my current plan has unlimited data but only 100 SMS (or something, I don't know because I don't use it).
But the important detail is that I'm not in the US, and this is what you're missing. In the US for some reason SMS became cheaper, in the rest of the world data became cheaper, which is why still to this day we pay for SMS but get unlimited data whereas in the US it's the other way around.