I highly Respect Mr. Barr and whatever he has done for the hobby. During his Era and whenever his method was born, it was designed to keep things simple without the need for testing, worrying about the nutrients etc. it was solely or primarily focused on dosing excessive and plant will use whatever they need. while I agree that this method attracted many hobbyist during that Era and I was one of them. Later as I advanced in the hobby, I learned more and more about the plants and highly focused on fertilizer and nutrients. we live in different Era now and things has changed over time, there are more scientific research, technology, things are more advance compared to what they were during Mr. Barr's Era. While Mr. Barr's Method is good for newbie/Beginners or keeping things easy and simple for the user. but, it may be lacking in many aspects. primarily, because this method was never designed to look into those aspects. we live in different Era now, where we have more tools and technology to dig deep into plants, nutrients and fertilizers.
there are several different ways to setup a low tech tank, it depends on the user what they are trying to achieve, many methods can be applied including whatever Mr. Barr has suggested. In my opinion Mr. Barr method may be bit outdated and may require some modification.
Quote from Mr. Barr:
"Based off of my testing, I'd estimate close to 5 to 10 times slower than a CO2 enriched tank at 2-3 w/gal. This rate of growth is such that the fish waste alone is enough to supply the needs for the plants. If we added more light then the CO2 would start becoming a more limiting factor and allow algae to grow better (algae need higher light to grow well in non CO2 enriched systems whereas the plants are much more limited without CO2). A lower light level is required, generally about 1.5 to 2w/gal is good."
I may have different opinion on this one. usually high light low to no CO2 isn't the problem. but under such scenario usually higher nutrients can become a problem. Mr. Barr usually advocate that nutrients doesn't cause algae, I highly disagree with this statement and everything that I have studied or tested up until now contradict with Mr. Barr's finding.
"Rather than suggesting allelopathy, Fe algae limitation, or PO4 limitation, I will say none of this exist. Rather, non limiting nutrient levels for plants will provide better conditions."
again, this is a big statement. both Fe and PO4 are well documented to cause different kind of algae's. suggesting non limiting for both P and Fe is likely to result in precipitation for one or the other or both, the end result being both being limited.
"Same applies for CO2 enriched systems, they just grow faster, but in both examples, the algae are never limited, algae is indirect, poor plant growth typically leads to algae blooms, thus plants define the system, not nutrients. When plants do poorly, they no long define the system, and algae can grow."
I agree with the poor plant growth being one of the causes for algae. but it also cannot be denied that you can have both algae and plant growing well at the same time. nutrients actually support both algae and plant growth, so we cannot say that nutrient don't matter.
"We can add KNO3 and KH2PO4 and show that in a non CO2 tank, excess PO4, NO3 (and Fe) do not cause algae blooms. We can add NH4 and induce a bloom just like a CO2 enriched tank."
this is likely due to combination of things, precipitation is one of them. excess PO4, NO3, Fe not causing algae would be incorrect statement without fully understanding the overall picture. while for whatever reason NH4 is a major contributor of algae? this is also an incorrect statement when not looking at the overall picture.
"We can also add Fe at high rates and also not get any algae. This assumption and knowledge frees us from limitation of nutrients which ultimately does more harm to the plants' health and well being, allowing a better environment for algae to grow."
again, this is a big statement regarding high Fe not causing any algae. when such scenario occurs, it occurs due to improper water parameters that will interfere with the Fe. weather its high PO4, High KH/PH. But Fe not causing any algae is also incorrect statement.
am not saying Mr. Barr is wrong at whatever conclusions he came up with during that time. But I strongly believe that they were rather results of not able to see the overall picture or lacked the understanding of every aspect, either from the lack of tools, data, research or technology. similar to if you were to look through the telescope 100 year ago, you would probably only see the moon through it and came to conclusion that there is only earth and moon. 50 years later with the new research, data, tools and technology, with the new telescope, you can see Mars, Venus, Jupiter etc. and now you know that there were more planets other than earth and moon. as we advance, we learn about new things and find new things that we previously thought didn't exist. My own conclusions regarding plants, fertilizers, nutrients are subject to change as we learn more and more. but am not going to make conclusive statement such as "Nutrients doesn't cause algae" because this statement is incorrect and can be easily falsified in the modern Era.
The best Method is when you do your own experiment and learn from it, there is no perfect method out there. 
... But seriously, at least I have learned - in large part thanks to the luminaries on this forum - that a whole lot more goes into being successful (or at least more successful) with a planted low-tech aquarium, such as maintaining a stable healthy microbial community, stable and appropriate water parameters, aeration, nutrient distribution and of course appropriate fertilizer dosing based on the specifics (hardness, alkalinity/pH etc.) of the tank and in the right ratios when applicable - and a whole lot more... and how all these things relates to our livestock in addition to our plants. All topics that keep UKAPS interesting - at least for me.
