The biggest downside I think is the inaccurate keyword volume sometimes. Previously, I was only using Google's keyword planner and it gave us more precise volumes. I guess it's easier for Google since it's their own tool and they can give better numbers. This confuses us because in Ahrefs we may see potential in various keywords but in the long run, after our articles are published – the traffic is not what we expect sometimes. Though, it's accurate enough for the most part.
Basically, Google shows the autocomplete suggestions whenever you start typing anything into Google search box. It is in Google's best interest to show the most relevant keywords in the autocomplete suggestions. Keywords that would help Google to retrieve the most relevant websites and help users find the most relevant content for their search query.
Utilize the "broken backlink" section. Utilize the ability to isolate lost and gained links by date. Let's say you have drops around October. You could go to right before that and specifically isolate good links lost or bad links gained, etc. They also have a good amount of helpful online resources for learning how to use the tool. Great graphs show overall trends for linking domains or linking pages. Check out the ability to sort by AHREFS' quality statistics to help analyze quality/low quality links.
AHREFS is certainly a great tool for bloggers and internet marketers. You have explained every functionality in great detail. I liked the link intersection part. It provides ou with a great opportunity to get backlinks from sites which are usually linking to your competitors. Further, its adds to the fact that these types of backlinks would be easier to get as compared to the ones that we search manually for any website. Plus, these would be niche specific too!