Why does low frequency RFID have a short read range?

Because RFID doesn't work based on wave propagation. It's thus not actually a radio system (despite working at "RF"=Radio Frequency).

Think of an RFID tag more as the secondary side of an air-core transformer, where information is transmitted by the tag changing the amount of power it draws from the primary side of the transformer, or by charging a energy storage (capacitor), and then exchanging the role of secondary and primary side of the transformer.

Because we're not talking about a wave propagating away from antenna, but about a coil coupling into a magnetic field, the decay in power is even worse than the distance² for free space loss, and after a couple of cm, practically no effect of the tag on the reader can be made.

You're confusing radio communications through the air with coupled inductors.

To communicate through the air using a 125 kHz carrier you would need an antenna of around 1/4 lambda so about 600 meter long in order to transmit that 125 kHz effectively.

Obviously RFID does not work this way.

RFID uses coupled inductors which means there are two coils (optionally with a magnetic material in its core) which couple to each other magnetically.

For this coupling to be effective, the distance can only be a few centimeters.

Simply put, the antenna does not radiate - it operates more as a coupled inductor. The coupling drops with \$r^3\$ rather than \$r^2\$ (if I remember right).

You have calculated the wavelength, so you can see how small the antenna is as a fraction of the wavelength.

With larger antennas, maybe a few meters, and higher transmit powers, its possible to get ranges of hundreds of meters using near-field communications. This is used for example in cave-radio - since the near-field does penetrate rock reasonably well.