The problem is that to cure them you really do need to take the underdrawings off, retighten the wedges and (re)glue them as well as possibly reglueing the glue blocks - things you can't do from above. This shows the sort of thing you'll see if you view closed riser stairs from below:
You can clearly see the wedges beneath the (softwood) treads and behind the (plywood) risers as well as one of the glue blocks. There are generally 3 or 4 glue blocks behind the riser/beneath the tread and these are rub glued so they can detach:
If you look aty how thin the risers are (often just 1/4 to 5/16in - 6 to 8mm - plywood, or maybe 1/2in - 12mm - softwood) and that they are often grooved into the underside of the tread above, and the back of the tread below (or simply nailed to the back edge as in the example I've posted), it stands to reason that trying to pull such thin stuff together isn't going to work that well.
PU glue might well expand, but it doesn't set rock hard, rather it is still a bit spongy, so by drilling and injecting it you might get a temporary fix, you might not. There are just no guarantees that it will work.
One of the few things I've found to work
if the creaking is at the stringers is to drill and countersink a couple of screws at an angle into the ends of the treads near where they meet the stringers. This has the effect of pulling the tread down onto the wedge and into the stringer, but it isn't pretty. It can also leave you with a gap along the edge of the tread where it is housed into the stringer and can damage the connection between the riser and the tread where the glue blocks are, so
only really suitable as a temp fix if the stairs are to be replaced
I'm afraid that in this case the old saw that if a job is worth doing, it is worth doing well really does ring true
