Rigidity of the blade has little effect on straightness of the cut. That is controlled mainly by position control of the saw. Normally only the tips of the cutting teeth contact the material being cut and the blade will cut in whatever direction it is pushed or guided. A wide blade, like with a hand saw, will be guided by the kerf, somewhat, but only after the kerf is established.
Sawzalls are not designed to make particularly straight cuts. They are designed to make free-form cuts. If you want to make straight cuts with them then use the widest blade possible and a guide fence to control saw position.
Other factors that control cut straightness are operator skill, uniformity of blade teeth and sharpness and uniformity of the material being cut. Until you understand how a blade cuts you cannot develop the skill to control it. Note that Sawzall blades are not straight. The tip of the blade is canted forward, so that as it strokes up, the cutting teeth progress forward in the cut.