All swords are tempered to flex, sanjuro_ronin
If a blade doesn't flex, it's too brittle and will snap. This is a great misconception about modern swords, as people don't hit them against each other anymore.
The modern epee and foil is just like the historic ones, save for the button. Back when I used to work at American Fencers, we sharpened epees and ran them through plywood. The saber is much skinnier, so it's not quite the same.
David Jamieson: It's actually pretty easy to find crappy blades. China-made fencing blades were notorious for a long time, but I've heard that they are much better now. There's no machine to temper blades - it's still all done by hand - so a veteran fencer will pick through the stacks to find good steel. By Paul, do you mean Leon Paul? I personally never cared for Leon Paul equipment. I always leaned to the German-made stuff like Uhlmann and Allstar. Mind you, I haven't fenced in years and the market has changed considerably.
You're stuck in the 17th century
Look at the 18th and 19th century foils and epees. The blades are not significantly different in terms of flexibility. I've seen colichemardes with more flex than some FIE foil blades. Foil and epee are point weapons, not necessarily edged, so you don't really parry in the same way. Blades do break in competition. That's actually the most dangerous part of the sport. But you wouldn't parry a 'live combat blade' in quite the same manner as it's point work, not edge work.
I studied with a pupil of Aldo Nadi, so yes, I've read On Fencing. In fact, the person responsible for the recent reprint of that work, Maestro William Gaugler, was my tutor for my provost d'armes exams.