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It's well understood that you need some carbon to get well tempered steel, and put flex into the blade for durability. (Brittle swords break easily.)
But is there any use of the flexibility inherent in swords?
In most cases, sword flex is only for the sake of durability and excessive flexibility is likely to interfere with doing proper damage with your blade. A major exception is the urumi, or "whip blade", where that flexibility is used to use it as more of a "soft weapon", able to make more use of centrifugal momentum and to curve around defenses.
As discussed here and in other parts of the Internet, the flexible blades you see in Chinese martial arts demonstrations and in movies are not historically correct, and are built that way entirely for visual appeal and for a lighter blade for faster movements.
There are two types of steel, hard steel and soft steel.
The purpose of hard steel is edge retention. The purpose of soft steel is absorbing shock. The purpose of blade flex is so the sword does not shatter on the first strike.
Here's the most basic thing about swords, ANY SWORD, no matter the culture. When they hit too many hard things, they stop being sharp. In movies, those photogenic edge-to-edge sword fights make swords appear indestructible, it's good drama. IN Reality a fight with blade on blade action quickly turn any razor-sharp blades into nothing more than a glorified stick. After a few sword strikes, chips and damage will occur and ruin the blade. That's why Japanese sword smiths devote especially extra attention to sharpening blades. But if the sword cracks extend past the core, if the cracks are sufficiently deep the sword is ruined forever and typically has to be reworked or recycled. Real sword fights focus on parrying, diverting or stopping blade strikes or with the non-sharp end being struck. Lots of antique samurai swords have strike marks on the opposite side. European sword fighting focus on thrusting, rarely slashing (less the opponents are unarmored), by the 14th Century AD, Plate armor was abundant on the battlefield rendering slashing techniques largely outmoded without heavier swords (falchions, etc)
Modern manufacturing and steel made from billet, has taken most of the guess work out of sword making. Making a sword from scratch is difficult. Making a sword from billet, is a lot easier. The Laminate sword making is the art of folding layers to make an intermixed series of layers of hard and soft steels offering flexibility and edge retention. The Japanese did sword folding by virtue of their terrible furnaces. They used smithing, because they could not achieve the temperatures needed to purify the steel to desired characteristics so they beat it into submission. If you have good quality steel, you don't have to fold anything. Japans first steel swords go back to the 5th century AD, Europe had steel for 1100 years prior, they used laminate folding six centuries before Japan. Then abandoned the technology for a better process, "Spring Tempering" which produced "Spring steel" which is phenomenally better.
