Your description of coax as lossless is not correct. Yes as you describe any length of coax maintains it's impedance (in this case 75 ohm). The reason this is advantageous is for power transfer. Without impedance matching on the output driver and cable system and input. Some signal would both reflect (cause interference) and not transfer well (power loss). But that is not so say that there is no loss in a coaxial connection. There definitely is line loss which presents itself as a loss in signal strength without a change in impedance. You still get the most signal transferred that is possible without knowing beforehand how long the cables will be. This is the design constraint the drove the creation of coaxial cable. Shorter cables will always have higher signal transfer. Not to say that that signal loss is prohibitive for even distances of 100 feet. Especially for a digital signal. You are only left with the issue of digital signal timing.
