My guess is that your router has already been in the hands of an
end-user.

An astute conclusion: the unit is "factory reconditioned."

The trick with the cloth and pliers worked. Got the collet out. After
I put the 1/4" collet in, however, and put the nut on, it won't close
tight enough to hold the 1/4" bit.

This is why I waited a year to get started. The crawling before
walking is painful. ;-)