I just finished my first quilt with significant half square triangles (240 of them!), and I had no trouble with cutting squares slightly oversized, cutting down the middle, and carefully sewing the pieces on the cut diagonal. The fabric was well starched, and I handled the cut pieces very carefully. I pressed and then trimmed. I didn't cut more triangles than I could sew in one session to minimize the handling. It seems ridiculous for the pattern designer to give you all those bias edges!
Pam