They absolutely should. G-meters are already compulsory in lots of high-school football leagues.

While the NFL is finally coming around on concussions, I think information from G-meters might be something they would rather not know. We all know the game is violent and NFL fans love a great hit. I don't think people want to know just how violent it is though.

I find that reasoning quite disturbing. Shouldn't the players health come first?

In a business the money usually comes first, and the NFL is a business in which there is surplus labor available and which has a tradition of replacing broken bodies.

It is the rare game which has no injury which causes at least one player to miss the next game.

Players are mostly a commodity the business of football. There are exceptions like the Aaron Rodgers or Tom Bradys of the world, but in general there is always another young guy waiting for his shot to play in the NFL.

The average NFL career is under 3 years long. And those guys typically don't even make that much money given the amount of post playing medical expenses they incur. I've had long conversations about the NFL with ex players (quite a few went to my old gym) and none of them would let their kids play football at any level because of the injuries that inevitably occur to everyone who plays. I think that's pretty telling.

Did anyone care about the health of the gladiators?

No, but we're not in Ancient Rome anymore.