True, and it is a little frustrating that DSC couldn't simply be a 23rd-century show that has just a few vague references to TOS (just enough to tie it to the franchise).True, though so far Discovery has yet to prove this and exist on its own merits. Hence why the writers felt it necessary to send the characters a 1000 years in the future.
However, the second part of my post above I think could be the answer to why the showrunners felt the need to jump the series forward ~1000 years. It might be because they wanted to open up a whole new era in which they could set their own part of the franchise with multiple series, much like Berman Trek set up shop in the 24th century with three series.
By jumping DSC forward, the show could act as that connection between the existing Trek universe and a new extended trek universe taking place in the 33rd century.