Not disagreeing with your larger point, but a nitpick: at these levels (postdocs, research scientists) the relevant university positions will be funded by grants, in fact largely from the NIH. University budgeting doesn't have all that much to do with it.

Now, postdoc salaries are set by a combination of university policy + whatever the grant budget says, but grant proposals are also assessed based on how much they ask, and postdoc salaries will be set by whatever NIH actually awards the PI. In the end, for NIH to pay their early career scientists more without creating problems for itself (by competing with groups it funds), it will likely have to increase postdoc pay across the board. This will likely add some upward pressure to postdoc pay across fields, since many universities do look at entry-level NIH postdoc pay as a reference.