Very much agreed, but then you're stuck with ensuring all the pieces of DNA are faithfully transmitted through the next replication. Essentially you're proposing having tons of 1kbp chromosomes, so you're shifting the problem from having a hard to handle piece of DNA (the longer the harder it is to have it not sheer/break/otherwise get damaged) to faithfully moving around lots of tiny pieces of DNA, and maybe depending on the system needing to guarantee not losing one of them entirely, or ensuring that the copy number of each one doesn't deviate too much from all the others, or both.

I think yours is probably the right way, though.