For Career mode (just pick where you want to go and who you want to work for) they expect you to start over after reaching your personal end goal.
The story campaign starts in 3015, with the career you choose a start point that can be several different times.
Since the dlc chains are tied to canon story events, and the in-game news reports follow the established canon time line, having them happen at other times would feel out of place.
I do get the feeling that they expect most of the people buying the dlc to be playing career mode, not the story campaign.
If you start a new career (or campaign) with all the dlc you can take part in some of the historical events in the Battletech universe personally. While still developing your own unit.
The Kestrel Lancers mission chain was really fun for me personally because I’ve read the books that deal with fourth succession war and it was neat to take a personal part in it.
You can import your unit from the story campaign into the career mode if you want to play all the content, but keep your mechs/pilots.