I took your advice, and here's what I found:
Purple=Lakers, Red=Jordan, Green= Super team Era.
The ratings have trended downward since Jordan stopped going to the finals. Jordan's popularity transcended the NBA. He was a world-wide cultural phenomenon and I don't think it's fair to compare any other NBA player or team to Jordan in terms of ratings and media attention to the NBA.
That being said, the Lakers (and Celtics) drew the highest ratings ever (pre-Jordan) and set the table for what Jordan was able to do going forward. The Lakers were a very large part of the NBA's high ratings and overall jump in popularity. You could debate how important the Lakers being involved was, but I don't think it should be understated.
Post Jordan, the ratings fell below what they were before the Lakers-Celtics era. The lock-out contributed, as well the Jordan bubble burst (no Jordan = a large amount of fans not watching anymore). As soon as the Lakers come back into the championship picture, the ratings go up two consecutive years. 2002 went down (maybe people were bored with the Lakers winning, maybe they didn't think it would be a competitive series with the Nets, or maybe complacent Lakers fans thought winning was an after thought and didn't watch)
Post Lakers 3-peat, the rating hit an all time low. The ratings shot right back up with the Lakers in the finals the next year (Malone, Payton, Kobe, Shaq proto-super team).
The next 3 years, the ratings fell below what they had been with the Lakers recent involvement. The 3 years after that, involving the Lakers, saw an increase in ratings, with a slight dip in the middle.
Enter, the super team era. Lebron goes to Miami. The ratings dip, but only slightly. Then, the last 3 season with Golden State. 1st two seasons drew slightly worse rating than the 1st two seasons of the Shaq-Kobe 3 peat. Average viewership was higher for Golden State's 3 year run.
From what I can see, when the Lakers are good the ratings go up.
I am legitimately perplexed how you could say "But they're a long way from being the "biggest brand in the NBA'". A long way? You think there are multiple teams in the NBA that are a bigger world-wide brand than the Lakers? IMO, I think you might be letting your personal feelings about the Lakers cloud your judgement in regards to where you place them as far as brand power in the NBA. The Celtics are a big brand, but I wouldn't even say they're the biggest brand in the Eastern Conference. The Lakers are hands down the biggest brand in the Western Conference, and I don't think any other team in the east comes close. The Celtics had Larry, the Lakers have had Kobe, Shaq, Magic and Kareem. The fact that the Lakers have had so many all time greats, basically 4 of the top 20 best NBA players of all time, fairly recent, puts them at another level of recognition as a brand.
As far as the Knicks go, I completely agree. The NBA would be better if the Knicks could get it together and be good. If the Knicks and the Lakers are good at the same time, the NBA is much better. If you're saying that the Knicks being good would make a bigger separate impact on the NBA than the Lakers being good, I think that's debatable but worth the conversation.