The convention of using LSB on 160, 80 and 40 and USB on everything else goes back to the early days of SSB.
That part is true.
Within the transmitter, the signal was generated as upper sideband in the 8-9 MHz range.
One or more mixers then brought the signal to the correct frequency.
On 20 meters, for example, the 8.3 MHz USB signal might be mixed with a 6MHz signal, the output would be the SUM of the 2 signals or 14.3 MHz upper sideband.
That was a common arrangement.
On the other hand for 80 meters, the same 8.3MHz USB signal would be mixed with with a 12 MHz signal and the DIFFERENCE would be 3.7MHz. Since we are 'subtracting', the original USB signal would be inverted to LOWER sideband.
I don't know any transmitter that did it that way. Not one.
I have heard this explanation more than once and it does seem technically (if not historically) sound.
But it's not what happened at all.
First off, it should be remembered the late 1940s the bands, subbands and licenses in the USA were somewhat different than today. In those days, the US ham bands were 80/75, 40, 20, 11 and 10 meters. 160 had been a popular ham band before WW2 but had been taken over by LORAN and we got it back in bits and pieces over several decades. 11 was given to hams as a sort of compensation but was shared with industrial, scientific and medical machines. 30, 17, 15, and 12 meters were years in the future.
On top of all that, 40 meters was all-CW, no phone operation allowed. So US 'phone hams focused on 75 and 20 - which were narrower back then.
The origin of the LSB/USB convention is what G3RZP posted: the use of an SSB generator in the 5 MHz range and a VFO or crystal oscillator in the 9 MHz range. This was done in the late 1940s. With such a system, the sideband inverts on 75 but not on 20. Both bands covered.
The original filter method used an LC filter down around 20 kHz, and needed two conversions to get to 5 MHz, followed by a third to get to the ham band. Lots of complexity but it worked. Crystal filters of the necessary characteristics did not exist yet, and mechanical filters were only good up to 500 kHz or so.
The phasing method came to the rescue, with the development of the Dome audio phase shift network. For some reason, it became popular to generate the SSB at 9 MHz and use a 5-6 MHz VFO to convert to 75 or 20. This scheme worked on other bands too - mix 9 MHz SSB with the third harmonic of the VFO and get on 40 or 10, mix with the second harmonic and get on 15. Commercial exciters such as the Central Electronics 10A, 10B and 20A appeared as early as 1952 using this method.
With the use of a 9 MHz SSB generator and 5 MHz VFO, the sideband DOES NOT invert when switching bands! But with a phasing-type generator, this is no problem because a simple phase reversal in one audio channel does the trick. A DPDT switch is all it takes.
There is a persistent urban legend that the USB/LSB convention came from the use of a 9 MHz SSB generator and 5 MHz VFO to get 75 and 20. This is a myth, because sideband inversion doesn't work that way. You only get inversion if the local oscillator is higher in frequency than both the input and output signals.
73 de Jim, N2EY