I tend to agree that it does not make you a better mixer. I think it just makes you learn to get the most out of what you got.

but at a certain point,
for sure,
you KNOW that what you have is not cutting it,
and you step up.
 
nothing makes you a better mixer,
except for mixing.
 
and that takes time and experience......
and proper gear

You can still learn to be better mixer even with underpowered technology.  For me it worked and was a sort of training ground.  Like working with only 4 tracks but with careful bouncing to a two track machine and back and adding in stuff as you bounce and transfer back and forth I was capable of creating very high quality mixes that sounded like 9 tracks.  All from a 4 track machine.
 
Where this plays out now is how I might set up and prepare buses within a complex mix.  I was used to making stereo stems before that allowed for extra material coming in later.  Had to because of the track limitation.  You can apply that knowledge to how you mix your buses today.
 
I also learned how to preserve a full stereo image right across.  I liked stereo early on and wanted to use it.  You can plug the stuff you learned that way right into a modern technology approach as well eg like using a VU meter.  Take it from the analog world and plant it directly into our current digital one.
 
The lack of technology can play out in use of effects.  I only had a homemade stereo spring reverb and a Roland Space Echo so you become pretty skilled at creating a very good effected vocal sound with only two effects processors.  Working with echo chambers which was the norm back in the days made you skilled at creating reverb like effects with echo.  That still works today.  Making wide stereo images out of mono sources that are robust and sum perfectly was another thing I got into a lot before.  It still works well now.  I was always trying to make something bigger than what I actually had.  But yes of course once you do step up and get everything you need it all becomes easier and faster too.  And you still continue to learn to be a better mixer for sure.
 
Before we had to work the technology to get to where we wanted to be.  It was clearer when you arrived at that point sometimes.  Now it might be too easy for the technology to blast way past that point and you are going way too far then.  Learning the way I did with underpowered technology helped me to keep that in line and you can see it and prevent it too.
 
I am sure there are other ways to get there. There must be and this in itself is interesting.
 
 

I enjoy reading about the methods of the past Jeff, keep them coming.  Your responses are like reading articles in Sound on Sound magazine. Plenty of good reads about how it used to be back in the days of 4 and 8 track machines along with their production techniques and of course the great performances. They produced great sounds which probably had something to do with the craftsmanship of the equipment made back then. Tubes, hand wiring, etc. I have been lucky enough to visit Sun Studios in Memphis and they have a huge display of old equipment. Of course I didn't know what a lot of it was, but it looked solidly made, heavy and all with big knobs. There's something about the sounds of the past that's so hard to replicate these days even with all our technology. Probably the more experienced mixers of our day would say I am wrong.

Everything I have i go off Craig's List or Amazon clearance deals. I do most of my work with midi drive modelers. And most of that is done on a Toshiba Qosmio (mild gamer) ($500) laptop. I
 
like doing my initial mixing on it. For me it seems easier to hear the problems on that than on the Aleisis M1 I got for $100. Later I do go there for final.
 
I find that if I try and find the mix on the better system I have to listen much harder. Any I get to work anywhere with the laptop.
 
For me doing things to conserve processing is a blessing, because I am less prone to fiddle with it. I record synth sounds to aux or freeze depending. But I do it to live with a 5 year old cpu with 8 meg.
 
Adapt or die I guess. I have been pleased with my hand me downs. Sampling instruments (AD 2 & Dim) are frozen and unfrozen at will all to keep it doable and smooth operating. 
 
I should mention that the laptop does have a little sub woofer with fancy speakers they sound nice on Netflix.

This sums it up quite well. Just watched an interview with Jack White and he quoted
 
There is more creativity when there is less opportunity.....

i know several folk who tried to learn how to mix on sub-standard gear,
and in the end, simply learned bad habits, 
and making wrong assumptions.
 
especially with low end issues.
 
 

and gear is one thing..
having the right environment that you can trust with your monitors, is another equally important issue,
and the two are tied together at the belly button.
 
 

And I know some people myself included that have created superb mixes with very limited gear.  Nice bottom end and all so that argument goes the other way too.  I bet you Bats is also one of those people.  I bet you were doing pretty decent mixes right back at the start with limited resources.  It shows because of the quality of the mixes you are doing now for example.  I am sure much earlier for you those techniques have worked in your favour.  Of course the better resources do help now for sure but it is easy to under estimate the importance of how we started off.
 
A good example of this is for me I only had 4 tracks to work with and spent years learning how to balance just 4 sources.  Something that simply does not happen today.  The kids I teach in sound engineering for example are thrown into a mix with 50 tracks and they wonder why they cannot make sense of it straight up.  The skills I learned in balancing a very small number of tracks have flowed on slowly for me. I went from 4 to 8 tracks for many years and then up to 16 and then 24 of course.  This was a real nice progression.  I cannot recommend it highly enough.
 
Good monitoring is essential of course and even for me right back at the start I had pretty decent speakers to work with a good sounding room.

So,
after thinking about the OP for a while, I must agree with the masters, yet with a serious caveat.
 
In the world of economic censorship, we must be highly discerning.
 
Just as money thrown at a problem may or may not solve anything, an under powered system may solve something.
 
I imagine I may have lost you by now, but for those who like a little intrigue, hear me out.
 
 
That which is achieved by having a low powered system is of greater value than all the gold that the Universe may provide. Having a low powered system teaches one the art of patience.  Money can buy immediacy, but often not, money ill spent will render palatable sludge.
 
Imagine a soul, with a one string guitar, lamenting the position in life they manage.  The blues came from such humble beginnings, and we love scatchy old blues records
 
For every thing there is a sweet spot.  For those of you who are under powered, work with the tools you have, find the sweet spot.
 
Much is made about bling, but bling is fleeting, and also a nickle and dime existence,
 
So have patience, click not excessively or randomly.  Give your under powers a breathe to catch themselves.
 
Great music has been revealed by lesser means than the technorati may coax you to believe.
 
Hit record.  Express yourself, burning up heart and soul.
 
Jesse Q. Screed