If you think about it a bit, just using biomedia is a poor idea.
What is the point of biomedia? Having a place for beneficial bacteria to grow.
What determines the quantity of bacteria that can form? How much room they have, AKA the surface area of the media.
Consider what makes good biomedia? Lots of surface area and to do this, media is often porous by nature. Ceramic media for example.
Back to the filter floss - you say it fills up with junk fast and cuts down on the flow rate? Would you rather that the biomedia become covered with all that stuff instead? How well would bacteria grow afterwards?
IMO there are only too kinds of biomedia that can do alright without dedicated mechanical filtration before them. They are sponges (which provide some amount of mechanical filtration inherently and can be squeezed out) and bioballs (which are not porous and can be easily washed). I do have some box style filters and IME they do best filled about 2/3s with biomedia and 1/3 floss. Yes the floss gets dirty, but that's the idea and it's easy enough to change.
