I have a fairly high-resolution monitor. I always bring up the Library via the hotkey (Ctrl-L). Unfortunately, it always comes up at the same, too small size. It does remember the columns I've selected to display and their order. It should also remember the size and position of the window.
Note that "layouts" (a poorly named feature if ever there was one) are not the answer. I may bring up the library at any time within the context of any number of explicit or implicit layouts. I just want the window's size and position to be remembered.
Donnie