I agree on ALMOST everything you wrote, and certainly amateur calculators have to be used with a degree of circumspection. The Gedmatch calculators, for example, make more sense if you take a really close look at the spreadsheets. But still, different calculator, very different results - some of them hard to reconcile.
What I find much more troublesome is that the genetic LABS themselves don't seem to agree on much. 23andme says I am 49% Central Europe, when FTDNA makes me 69% British Isles (in Auvergne?). They don't even agree with... themselves sometimes! They change their chips, update your results, and what you get is light-years away from the previous version. Is that science? Science to me means: same causes, same consequences, mechanically, and indefinitely. OK, it's a science which is currently "under construction". But still.
Concerning very deep ancestry, to be fair we must also concede that at some point it must be hard to distinguish between, for example, WHG proper, the Villabruna-like WHG genes that back-migrated to Anatolia before the farmers started moving, the WHG gene substrate in EHG, the CHG inherited by westerners from Kura-Araxes migrations via Anatolia, the CHG inherited via the steppe... It's all the same basic "bricks" that reappear in various places in our genetic buildup.
Why don't those guys sit around a table, discuss things, and homogenize their procedures? They might lose in creativity, but also gain in credibility. And we people might begin to look at our results as reasonably reliable.
Personal genomics are separate from what the academic labs are doing with ancient dna, where there is general agreement on the major issues, I think.
You're right that the results are very different by company when we're talking about personal genomics. The actual raw data is, of course, the same: it's your genome. The difference is the algorithms and how they group the reference samples, and indeed which reference samples they use, and then how they interpret the results. There's also a difference in what precisely they are marketing.
They would each say, doubtless, that their method is better, so why should they change it?
In their defense, I think it's an almost impossible task.
There are too many layers, and most importantly political boundaries, often only a few hundred or even a thousand years old do not always equate to genetic boundaries. Take my own area as an example, what might be called the hinterlands of the ancient town of Luni on the coast of the Mediterranean in Northwest Italy. It was settled by Neolithic/Cardial farmers, then various Indo-European admixed Bronze Age groups, then Iron Age Gauls, then "Romans" from further south, then some Langobard lords. Let's not forget the Greek traders too. Politically, the people were first part of a "Ligurian" group, then part of Rome, then ruled by Langobards, then split between various medieval kingdoms: some areas ruled by Genova, the capital of Liguria, some by Modena of Emilia, some by the Tuscans under the Medici, some by all three. So, what are the people of the Lunigiana? Are they Emilians, Liguri, Toscani, all three or none of the above? I have ancestry from both Emilia and the heart of the Lunigiana, and even some from La Spezia itself, which has a lot of similarities to Tuscans. On every test I come out as half way between the Lombards of Bergamo and the Tuscans, but not very close to either. So, who is to blame that my fits aren't very good and some are downright terrible?
In terms of Italy again, some of the personal genomics companies have a Southern Italian/Greek cluster. That means that northern Italians would get some of that but also quite a bit of French or German and a lot of northern Balkan. If a company looks at the spread of the data and sets up a separate Greek and and also a separate Italian cluster you're going to get some southern Italians with a lot of "Greek", and some Greeks, especially Greek Islanders and people of the Peloponnese, with a lot of "Italian". Is one better than the other? I don't honestly know. Looking back on my example, if a company created a "Northern Italian" cluster instead of a Balkan cluster, a lot of Balkanites would get a lot of "Italian".
Do you see what I mean?
Or let's look at the people of the "Low Countries" versus England. Sometimes it's hard to tell which is which. Northern Europeans as a whole are more homogeneous than Southern Europeans. In Britain, for example, none of their specific WHG survived and almost none of the British Neolithic. So, the big bulk of their ancestry is Beaker, which is a combination of about 50% Late Neolithic (majority EEF/minority WHG) and 50% "steppe", with maybe 60% EHG and 40% Caucasus/Iran like ancestry. That's the same group that went into the Low Countries and France, but perhaps in France more of the EEF survived. There's a cline even in the Low Countries. Then England was invaded by the Angles/Saxons/Jutes, a related people with lots of "steppe", but with more "eastern" ancestry perhaps and drifted enough so that they can perhaps be labeled "Germanic" vs "Celtic". In some areas that becomes 30-40% of the ancestry. Then the Danes/Vikings arrive, who were thought to be very different, but were also Germanics. Then the French arrive, some from areas very "Celtic" like, like Brittany, some with a bit of "Viking" ancestry like Normandy, some from northeast France, and so more "Germanic", but some also from Aquitaine and other southern areas, who are a bit different.
Can you see where there might not be much difference between someone from eastern England and Jutland, or Holland? Or someone from Brittany versus Cornwall? Or looking south, someone from Aquitaine and someone from far northern Spain?
France is particularly difficult because so little genetic testing has been done there. There's an old sample taken from students at the university in Lyon and a few from somewhere in southwestern France. So, how are the French going to test? Well, given that a lot of them have quite a bit of "Beaker"ancestry and the British have as well, they're going to get a fair percentage of "English" or British. The ones in the southwest as going to have a lot of "Spanish" perhaps, and the northern Spanish might get a lot of French.
Those country designations are just names, arbitrary names drawn on a map. Yes, they are barriers to gene flow to some degree, more so in places isolated by the Alps and Sea like Italy, and therefore create some drift, and they're certainly different culturally, but genes are no respecters of lines on a map.
It's my opinion that we're almost asking these companies to do the impossible. If you want to know the genealogy of your family, where they came from for hundreds and hundreds of years, then a family tree is the best bet. You get more understanding of your genetics by learning of the different migrations to your ancestral areas than by some of these tests.
Anyway, that's my take on it.
I've been at this for more than ten years and that's what I've concluded. As for which companies are "better", imo ancestry and 23andme are the most reliable. At least with 23andme they don't just rely on the few samples in academic papers, but include the genomes of their customers. I think perhaps Ancestry is also starting to do that? I think My Heritage is terrible, and so is Living DNA, but again, that's just my opinion.