You have basically answered your own question:
they set the default voltage to a value so yhat you don't get a
floating high or low value.
This is especially important in TTL which needs to have defined inputs to have defined output(s). If there is nothing driving an input, or what would typically drive that input is in a high impedance (tri-state) mode, a pulling resistor is necessary to provide a definite level on that input.
Check out these basic examples, based on the components you mentioned...
simulate this circuit – Schematic created using CircuitLab
The Tx line is "pulled HI" by R1. This example works better in a multi-master setup, but the idea is the same. The master transmitter will likely first check if the line is HI or LO. If it is LO, the slave is probably holding it LO, so the master will wait with its output in a tri-state mode (high impedance). The opposite would be true for R2 the pull-down resistor.
If neither the slave nor master are tryint to transmitting anything, then their outputs will be "turned off" in the high impedance tri-state mode. R1 will pull the master Tx HI; however, no current flows through R1 because there is no ground to sink the current. As such, the master Tx line is essentially the same voltage as Vcc.
Similarly, R2 pulls the master Rx line LO, and since there is no current source on either the master Rx line, there is no voltage drop across R2 so the master Rx line is essentially grounded.
Using this Drive / Tri-State operation, the chance of shorting master Tx to Slave Rx is greatly reduced, if not eliminated. Long story short, using the ideal laws of pin inputs, there should be essentially (virtually) no current flow at all through R1 and R2, hence, no flow of electrons. However,