Well tbh, your post makes a lot of sense. I am using all these tools but to be honest everyone of these tool have their own pros and cons. But to be very precise, let me share some useful knowledge with you..
I have bought thousands of domains in my life for PBN purposes and according to my knowledge following facts are true:
1) Moz DA and PA is actually a lot closer to Google's liking or disliking algorithm, it's far more superior than the Ahrefs DR for following reasons:
Ahrefs DR actually emphasizes more on amount of backlinks, don't be shocked if you see a domain with thousands of junk nofollow backlinks with high DR. This is how their algorithm works.
But Ahrefs have a very superior backlinks' index. They have more data so I still prefer Ahrefs on any other tool when analyzing a domain.
2) Majestic has a good but smaller index than Moz and Ahrefs. But the TF metric is very beneficial, bcz it shows you that how many trusted(white hat backlinks) a website is receiving.
Majestic has hired some operators who actually manually review a site and give it a Trust flow according to its structure and ability to stop spam backlinks.
It also considers a site's OBL etc. So if a new domain is receiving 10-20 backlinks from very authoritative websites, then it can have a good TF of over 20 even with some 10-20 backlinks or even just one.
3) Use these tools like this, Moz: to search how good a domain can perform in Google(use spam score as well), Ahrefs: To check backlinks manually(since they have superior index), Majestic: To see how many trusted links a website is receiving.
That's it

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I hope this helps.