

This is a really great question! You’ve already got the underlying reason down too - all the various executive departments were created to distribute the enormous administrative burden of figuring out how to enforce laws that have been passed.
Interestingly, Congress is actually in charge of creating the various departments. The President is not authorized to abolish or create new ones, or to expand their jurisdiction or invent new powers, however they are responsible for proposing leaders to each and soliciting their guidance for topics within their domain. How this currently gets enforced is part of the issue however.
Independent agencies also exist that do not explicitly fall under the authority of the President. While the President can remove heads of departments for any reason, there is a much higher bar for removal of independent agency board members.
As the office of the attorney general is one of the government’s oldest, established during the first Congress, this may be a matter of combatting tradition more than anything else! This predates independent agencies by something like 100 years.
I should also edit in a clarification that the DOJ not being an independent agency is what allows it to be more partisan than something like the FTC. Also that an independent agency does not in and of itself entirely mitigate partisan politics from its decision making.

Not even calls to fix it, because they wouldn’t want to even imply their opponents could. Instead it will once again be a way to frame opposition to spending on programs that are positioned to improve lives, or to distract, with it being a “more important” topic than whatever initiative is being floated.