Because in 2003 most computers couldn't handle processing videos in 4k. Heck, even today many YouTubers still post in 1080 in order to help make file sizes more manageable. Since most YT is watched over a phone or tablet 4k is not necessary. Using a 2002/2003 computer the entire processor would be consumed for days trying to render a 4k video. Honestly, it couldn't even start since no computer had enough RAM to feed the processor the 4k content for rendering.
I can't even imagine trying to upload a 4k video back in 2003.... potentially over a dial-up connection. A 10-minute video in 1080 is usually around 2 gigs - so even that was unimaginable with upload speeds in the 100k/sec range (and dial-up was uploading at around 12k/sec)
next.... the computer. I bought a Gateway laptop in 1999 for $3000 - it had a 4 gig hard drive. Sooooo that entire hard drive couldn't store a single 5-minute video in 4k.
Finally... you have your media cards... back in 2003 a 64 Meg card was expensive. i don't remember exactly the cost but it cost more than a 128G card costs today (depending on speed). So that card could only hold a few seconds of 4k content... and ... this is big... most 4K cameras require writes speeds of around 60meg/sec (at the absolute MINUMUM - higher-end cameras need 150 meg/sec). So the card would need to have the ability to write nearly 100% of its capacity in less than 1 second.... and then it would be full.
soo... those are a few reasons why