I’m skeptical about one of the main premises of the article: that brand keywords don’t have a positive ROI.

Background: I took part in running millions of dollars of brand keywords for multiple companies. This is not what my business sells anymore.

I’ll explain my counterargument in two different ways: with an analogy, and with data from a project that I was tasked with figuring out whether branding ads had an ROI. I'm looking for responses that can poke holes and help me have a better understanding.

The analogy.
Imagine you own a Chinese restaurant. John Doe is in the mood for Chinese chicken dumplings. John is hungry and in a rush so he gets in his car and starts heading to the local restaurant area because he heard about your restaurant. There are multiple ways to reach your restaurant (same as when you search a brand name in different ways + product A/B/C). No matter which route John takes when he is looking for your restaurant, he will have to go through one of the many roundabouts (the roundabout is the first page of the google search results). John reaches one of the roundabouts that’s right before your restaurant. There are 10 exits, some of them lead to your restaurant and some of the lead to other places. Since this is a roundabout, you don’t get to see each exit at once, but rather go one by one. Each exit has a sign that states the name of the place and a small description. The information on each sign was put up by the local authority (google), which is based on what the restaurant initial provided but it’s relatively the same across all roundabouts that lead to the restaurant. Since John is hungry and in a rush, he tends to take one of the very first exits he comes across (similar concept to the amount of traffic the 1st search result gets VS the 2nd Vs the 3d). The problem is that your restaurant is not the first exit for every roundabout (i.e the 1st result in google). For some roundabouts, the local concierge is the first exit (i.e a number of brands I worked with had the 2nd result for certain brand+product keywords as the 1st result was taken by major informational or review websites). For some roundabouts, the local authority agreed to add a new exit as the 1st one you come across that has a digital sign which changes based on what every "John" is looking for ("yummy chicken dumplings") and leads to the competition (paid search ad that always shows up before the organic results and the title/copy changes based on what someone is searching). For other roundabouts, your restaurant is 1st but John searched for your brand + "product by the wrong name", so the description of the first result doesn't reflect what John is searching for and he skips it (because Google doesn't let you dynamically change the organic title/description as you are allowed with the paid ads).

The data. We stopped google SEM brand ads for 6 months, restarted them and let them run for a few months. We noticed that when we restarted the brand ads, the organic revenue decreased. The organic + brand ads revenue also fell by about 25% VS the time we didn't have brand ads running.
The key question was: Did the number of people searching for the brand decrease during the same time? If branded ads are 100% cannibalizing the organic ROI, then the organic search impressions (i.e how many times the brand's links show up when someone searches the brand on google) and clicks should have remained the same.
We looked at the top organic brand keywords that were responsible for 99% of the impressions/clicks the brand got on google. During the periods that we checked, organic impressions/clicks had fallen by about 40%.
So the number of people searching for the brand fell by about 40% and yet the revenue from the organic search + brand ads only fell by about 25%. If you crunch in the numbers, you'd see that we had about a 20% increase in organic + brand ads revenue VS purely organic revenue.

Last but note least...
I don't have the links to the following research with me right now but it's available online: (1) competitors bidding for your brand terms can steal a double-digit percentage of your organic traffic if you don't bid as well, (2) consumers think brands are more legit the more they see their results all over the first page, (3) consumers put significant weight on the first result of the page, (4) the message brands use to get the user to take an action can have a double-digit percentage impact on whether the user will that action or not. Bonus: the high CTRs from the branded keywords help overall google ads account health/quality which helps you get cheaper ads from Google, better positions, etc.