I think it's important to understand the timeline here. The footage we've all been amazed by was acquired by a collection of slightly-hardened small, light, high-quality commercial off-the-shelf (COTS) cameras, helped by a fast, very-low-power processor (I think a Qualcomm SnapDragon: this processor is much faster than Perseverance's main processors!) and cheap, copious, flash memory. The two guiding principles for the system were (from memory: they mention this in the press conference) 'do no harm' and 'it can't matter if it does not work'.
I don't know when the final decision to add this to Perseverance was made, but I will assume 2017 (three years before launch in 2020). Well, I have an iPhone 8, which came out in 2017. It has a camera module which would be pretty suitable for this, and its processor similarly would be more than competent. It probably doesn't have enough memory (32GB) but that's because I didn't need more: clearly it could have.
But probably they were doing component selection well before that: say 2015: so the right device to look at might be the iPhone 6s. This would also be pretty adequate I think.
Testing of components for Curiosity began in late 2004, and design was largely complete by November 2008 (Wikipedia), which I will take as the drop-dead date for anything like this: also three years before launch. If we assume that component selection was made two years before that again, we're now in 2006.
In 2004 the first GoPro was released: it used 35mm film. In 2006 the first digital GoPro was released, which could record for 10 seconds.
The first iPhone came out in 2007 It had a 2MP camera (could it do video? probably it could). There were 'smart' phones before that but probably the smartphone era really dates from this: a year after they probably had to make the component choice for Curiosity. In 2006 I think I had a Motorola Razr, which was a nice-looking phone. I think it has a ~1MP camera, and it could probably do rudimentary video. I have some pictures from it, which are terrible.
And in fact Curiosity did record the landing: MARDI could shoot 4 frames a second, and recorded the entire landing. I don't know if this captured video was compressed before upload: I would suspect not however, as it would have been very demanding for the computational resources of Curiosity (MARDI has 8GB of flash). MARDI is very definitely not a COTS system, and represents what was possible in the mid 2000s when things were being finalised for Curiosity.
For Curiosity to have recorded multiple video streams as Perseverance did would have required multiple, probably large, non-COTS cameras and computational resources which would probably have completely swamped the available power on the rover. This would have seriously impacted on the mission: it would have hugely violated the 'do no harm' rule.
So this is why. The amazing video we have seen from Perseverance exists because smartphones exist: that technology simply did not exist in 2006. Although it is hard to remember (especially if you are not old enough to remember), the technology that is now cheap and which we all take for granted was once extremely expensive, and before that did not exist at all.