As someone who's watch Trek First run since 1969 - your assessment is laughable.
Trek continuity had NEVER been cohesive to the degree you suggest.
The Kurtzman era is no worse than the Original Trek era or the Berman era when it comes to what they've done to or with Trek franchise continuity.
I think the Berman era was pretty consistent. They made changes but one can see almost instantly that TNG.DS9 and Voyager are all more or less operating in the same setting and world as each other. I would even say Enterprise was like that as well. TOS or more of it's own thing but even in the case so many of those characters played by the same actors did somehow find themselves in Berman Trek time period.
Kurtzman Trek feels more connected in this way to the Kelvinverse movies. Familiar characters and some of the same toys but all done in a more sleek and modern way. Not to mention the stylized Pillar speak as I call it, just no longer exists in Trek. Trek characters now talk like we do or sadly to often like teenagers do in the modern shows.

