Before the advent of HT receivers on the market with built in fixed and variable crossovers, the only way to attach a sub was through the high level inputs, only those who were fanatics would go for external crossovers at a high cost. The advantages of using the high level are there if you take a closer look. What happens is that by taking away the low frequencies from your main speakers and amps, you are giving them a huge break. The most power robbing facet for an amp is low bass and it is also the one which causes most dispersion in drivers. Most drivers today are 2 way with the mid/bass combined in one unit. The 3 ways are rare and fast disappearing. If low bass is taken out of the main speakers, the mid clears up due to less cone movement. This can lead to clearer sound. You can also do that by using the low level connection from your receiver to your sub and set your main speakers to SMALL but in this case, if you have good bass capable mains, it is a waste as the mains would be able to handle up to 50Hz with ease, this is where the high level input connection comes really handy by letting you do the variation to your taste and capability of the current amp/speakers.
The noise factor could be coming from the speaker cables picking up stray fields nearby from sources like transformers etc.
On another note, at least with Yamaha HT receivers(there may be others), by setting the bass out to BOTH and selecting the main speakers to LARGE, one never looses the .1 even when high level inputs are used.