Of the few razors I've had (ATT, Gillette NEW, Gillette Red Tip, Gillette Aristocrat Junior, and a few others), there are two stages in loading a blade. (1) Insert the blade, and (2) closing the housing so the blade is held rigid and flexed. It's assumed that the blade isn't going to move, since it's clamped into place and flexed.
Any se razor never seen one flexing the blade, oneblade even has a floating fhs blade. The half de blade razors do not flex the blade either afaik some tilt the head which gives a bit less control but more comfort.
I've not experienced any razors where the blade isn't flexed. For many razors, it's integral to the success of a shave. (Carts avoid the problem, since the blades never flex.) So I agree: rigidity of the blade is essential. A blade shouldn't flex or bend once it's loaded into a razor.
Which razors don't have this feature?