But it is of critical importance to have the sensors located at the right height!

At my school, I had to jump up quite a bit (and I am 6' tall) to get them to read the card.

In many installations of both hardware and software, the actual usage of the system is quite different from what was imagined by the designers. Prox card installers imagine people holding up cards on lanyards. They mandate it not be carried in a wallet, because "the magnetic fields of a credit card can erase it" and it might break if it's bent. In real life, only freshmen carry lanyards, credit cards use high-coercivity stripes and aren't damaged by the prox readers or cards, and wallets with IDs and credit cards are stiff enough.

Talk to your users about how they use your product and what they need! You will learn something!

The height's probably specified by building code re: disabled people, whether or not it's compliant

They also have longer-range solutions now and things that use Bluetooth instead of rfid for this. Works from a few feet away. I'm guessing that it's using some combination of Bluetooth MAC + signal strength.