Question about polarity-inverting preamps

You will see that I am technically challenged...

Many tube preamps invert polarity. Why don't (or why can't) the designers simply reverse the leads at the out jacks to make the polarity correct? Then we wouldn't have to reverse them ourselves at the amplifier or speaker.

I read somewhere that some preamps invert because it eliminates the implementation of another stage for the signal to pass thru. Maybe someone knows why this inversion occurs in the first place? The designers avoid the issue by having the accompanying model power amp invert too. Some preamps do offer polarity switches.
Many of these amps are single-ended, that is, they have one output signal referenced to ground. In such case, one cannot simply switch signal and ground to reverse polarity. The only way would be to add another stage which ain't the best way. Swapping the speaker leads does it better.
The above have it correct. Conrad Johnson and Blue Circle preamps are out of phase for this reason (less is more) and are among the best.

My moving coil phono stage is out of phase. Since moving coil cartridges have such a low output, adding the additional gain stage to correct the phase would add unnecessary noise to the phono circuit. To correct this I reverse the leads on the tonearm going into the cartridge.

Some preamps (Atma-sphere & Sonic Frontiers to name a few) have phase inverter switches to let you A/B the sound. This is a really nice feature. Happy Tunes!
Is that really "phase inversion" with the Atma & SF preamps, or are those switches really reversing the phase as in polarity?? If so, not exactly the same thing. We had a discussion on this a week ago. Search the other threads.

Those that own those preamps can test it. Play some music with a loud whack of a bass drum or something that makes the woofer on your speakers push out a lot. Then try it again after pressing the switch on your preamp. If it is inverting the phase 180 degrees, the woofer will now be sucked in a lot, instead of pushed out.

Here's some food for thought... in a single ended system the preamp's input signal is configured as a positive and a ground. To process the signal the preamp can only work with the whole wave, both positive and negative. So out of necessity the preamp inverts the incoming positive to generate the missing or negative half. To make the output useful at the single ended connector the processed wave must again become single ended, that is, split. Whether the positive or negative becomes 'the signal' appears to be arbitrary. My uninformed guess as to why the output remains inverted is that the inverter plays a part in the splitting process. Who really knows why?
I was going to let this one go by, but Rockvirgo's post begs a response. It's got a few problems.

On single ended inputs the signal goes both positive and negative with respect to the chassis. The preamp does not "generate" a missing negative half. There is nothing missing that needs to be generated and nothing gets split.

The job of the preamp is to amplify the input voltage and to have a low enough output impedance to drive the cables and the input to the amp. There are three ways to configure a tube. Common plate is commonly callled a cathode follower
Z means impedance.

common grid = input on cathode and output on plate
common cathode = input on grid and output on plate
cathode follower = input on grid and output on plate

======================= voltage =============== inverts
============= input Z ==== gain ====== output Z === polarity

common grid======= low ===== high ====== high ======= yes
common cathode === high ====== one ====== low ======== no
cathode follower ==== high ===== high ====== high ====== yes
ideal preamp ======= high ===== high ====== low ========= no

Overall the preamp must have a high input Z, high gain, and low output Z. As you can see none of the three configurations meets this requirement. To get around this problem, in a typical minimalist preamp you have two stages. The first is a common cathode which gives you voltage gain but inverts polarity. It also has too high an output Z. So this is coupled to a cathode follower that gives no gain but lowers the output impedance. The signal reamins inverted. To get it back to the original polarity would require another inversion. A lot of designers don't want to add another stage so they leave it inverted.

There are other design schemes but this is probably the most common used. Sorry for all the ======== but if you use more than one space in a row it gets reduce to one space.

Note to Audiogon: You have one of the most frustrating word processors I have ever used for posting ads and chat. Why can't you just leave the puncuation and capitalization the way we enter it???