Subordinate clauses headed by "With"

There are some subordinate clauses headed by with. For example:

A company can adopt a standardized approach or an internal models approach, with the former generally leading to much higher capital charges and the latter requiring regulatory approval.

the number of graduations by international students rose significantly in the 5-year period, with all universities seeing an increase, with the exception of Alberta.

Here are my questions:

1. What is the role of with in such clauses?
2. Do these clauses indicate a result/consequence? For example, the number of graduations by international students rose significantly in the 5-year period, with all universities seeing an increase as a result of increases seen by all universities, with the exception of Alberta.

EDIT: To make my question more clear, I modified the post. The original post was: There are some subordinate clauses headed by with. What is the role of with in the sentences below? And as stated by 1, is such a structure doomed to be weak and it has to be avoided?

One reason to avoid such a with phrase is that it is, itself, used to avoid absolute constructions, by authors who either deem their audience unworthy, or who fail to think of them at all. And so it is sometimes felt to be a less literate substitute.

Note: with phrases can be used to great effect, but the ones in your examples could be replaced with normal absolute constructions.