The short explanation is that HDMI is faster than “internet cable”
There is not a single cable called “internet cable”, there are cables you use for computer networks the common in households are ethernet in a copper cable like CAT-6 and for long-distance, it is an optical fiber.
The problem is that the data rate in ethernet is high but not as high as the other you mention.
The max data rate in the now common HDMI 2.1 standard is 42.6 Gigabit/s compared to the common ethernet today of 1Gigabit/s. You will see some 10Gigabit/s ethernet on expensive motherboards.
The 10Gigabit/s ethernet standard is from 2002 so when DVI was introduced in 1999 the max speed was 1Gigabit/s. DVI had a speed of 3.96Gigabit/s in the single line that HDMI adopted and 7.92 Gbit/s is the dual-link variant.
There is 40 Gigabit/s electrical ethernet too over the wire but it requires quite complex and advanced electronics. There is a faster optical standard but the cost is a lot higher.
HDMI is the same as DVI with a different connection and sound added. VGA is an analog standard.
For the same speed at the distance that we used HDMI, they are cheaper and better designed for video than to use ethernet. Ethernet has an advantage in max length but the electronics you need for the speed cost more than the HDMI.
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