Why did they use to call Kickboxing Full Contact Karate back in the day, and why did they stop doing that?

PKA coined it back in the mid 1970's, and when the PKA was resolved, a new label was created; out with the old and in with the new.

Ah, Marketing.

Ah, Marketing.

Ah, YES, indeed!!

Ah, Marketing.

Indeed, it makes it sound like you are learning a form of karate.

Kickboxing is kickboxing - karate is karate

Wait...Judo is full contact Kung-Fu

Depends on the country of origin; in Japan it originated with Oyama and Kyokushin. The moniker of full-contact, or knockdown, was used so as to differentiate what they were doing from the sundome shiai as propagated by the JKF, and which had become the prevalent model of competition through the 50s and 60s.

In the West, it was essentially synonymous with kick-boxing. Kick-boxing as we would recognise it was not introduced to the West until the 70s, and American Kick-boxing has its origins in the Karate competition of the 60s. When first introduced, as mentioned as being by the PKA, what was American Kick boxing and what was just traditional karate competition done with full contact was indivisible. However, there were already many celebrated karate competitors, and many Americans, or those interested in the sport at least, knew what karate was. It was easier to market it as full-contact karate, a twist on a familiar product, than to introduce a new word to the lexicon such as kick-boxing.

However, I would not leave it on such a cynical note. As mentioned, early American-Kickboxing and the full-contact karate propagated by the PKA was far from distinguishable from one another. Like Kyokushin, the full-contact moniker was just the most logical way to distinguish between what it was from what had thus far been.

Maybe it is a similar phenomenon to how in the early days of martial arts, every and any exotic Asian system was called "judo" and later on "karate". That combined with marketing. To popularize something for which most people have little to no reference, it is always best to try to make that new thing fit into a definition likely to be the understood by most.

It matters little to the public if that assigned definition is not exactly true. Back in the day before Taekwondo was widely known, many advertised it as "Korean Karate". When judo and jujitsu were first taught outside Japan it was called Japanese Wrestling and so on.