Stopping a bullet and protecting football players are two unrelated things.
For starters, players refuse to wear pads below the waist (well, save for the family jewels).
The helmets are pretty dang good for the motion they allow
Kevlar is always available for ares of the body likely to be subjected by near point-load forces.
It's just the human body really. Cartilage, tendons, ligaments, bone.... these things can take extreme loading...static, cyclic, dynamic you name it.
Some players last a season, others dont. Its a mixture of biology and luck
As a materials engineer, I can assure you this field has done as much as it reasonably can in terms of materials science to improve player safety. Designing a material that can resist the types of forces NFL players are subjected to without limiting their range of motion is next to impossible. I mean, I guess they could all play in tempered, bullet-proof glass bubbles...but what fun would that be? :)
Since the 1950's, our knowledge and application of plastics and various rigid & pliant composites....their use, properties, how to tweak their molecular structure etc. has increased dramatically. We now have materials that weigh less than more traditional materials, but also have the same stength and toughness; each with a variety of ...well "flexibility"(For example...take "spider silk". The stuff is capable of extreme extensions, but it also is one of the strongest materials (weight for weight) known to man. It all has to do with its micro structure...crystalline and amorphous regions blah blah blah I did my thesis on this i could go on for hours.)
Kevlar is essentially modeled based on the structure of various species of spider silk. Fibers reinforced in an amorphous region. KEVLAR has gotten better and better throughout the years.
Pretty much we just have better plastics and such that we no longer need the sheer mass and volume of a material to achieve the same force-stopping capabilities if you will.
Sandlot is a classic also.
ahhh, the good ol' youth years.
Do they even make movies that good for kids nowadays?