你的印象是错误的。表语形容词后记介词+wh-从句，介词通常都是可以省略的。而that从句不可以作介词宾语，所以形容词后直接跟that从句，不可加介词。

对于be worried而言，下面为COCA例句：

I was worried what you might do if I left, but now I don't care.

Her son had a hard time coming out because he was worried what his family would think. 

I was worried what I was going to see when I pulled the blanket back.

I was worried what you were gonna say.

Noe didn't have to resign but was worried what might happen if he didn't.