the black plastic (if its the same as mine) just directs the coffee to the spouts - no big deal since it doesnt add pressure to the extraction, it just stops the pressurised pinhole from drilling a hole in your cup!
It does trap a bit of old coffee oils, not much though if you rinse it regularly.
I have a bottemless pf from a cheaper Breville but it doesnt fit as well.
If you drill out yours (not too hard) you wont be able to go back to the pressurised basket if you ever want to (resale, other users?)
You could post a "wanted" in the for sale section and see what turns up.