Why don't TV/film studios and producers accept unsolicited material?

Why Do TV Networks Have 'No Unsoliciated Materials' Policies?
One reason:

LAWSUITS. Networks do not want to get sued because you thought they stole your idea. When creators pitch an undeveloped idea anybody could have come up with ... they think a show that has anything do with their idea was stolen from them. For instance, Marc Zicree was a writer on “Star Trek Next Generation” and he told us there were one, or more, lawsuits filed for every episode by people who claimed their ideas had been ripped off. Are ideas ever stolen? Yes. Does it happen as often as rumored? Absolutely not.

Also see: Help, Hollywood Stole My Idea (or Script)!

Screenwriters: Find An Agent (or Manager) with Script Contests

Getting representation from an agent or manager in Hollywood is not easy. You have to find someone who believes in you and your work, and you need to believe that they are both capable and willing to sell your work.

One of the better ways to get noticed by agents, managers and producers is script contests. ... it can lead to an offer of representation.

5 Script Contests Actually Worth Entering, Screenwriting Magazine, Sept. 16, 2016