Big brands always have very high site authority. Site authority is a relative metric which depends on the number and quality of backlinks a site receives. However, other factors such as topical relevance, content quality, EEAT (Experience, Expertise, Authority, Trustworthiness), technical SEO, On-Page SEO and many others can also be taken into account when evaluated by Google.
Here is the Lego.com SEO Domain overview:

What problems did I find?
Problem 1: Lack of organic traffic for non-branded searches
One of the most common problems for big brands is the lack of organic traffic from non-branded queries. Big brands are very well known and attract a lot of visits from Google or directly from people explicitly searching for the brand name.

Lego.com has only 5% non-branded traffic.
It’s not a bad thing to have a lot of branched traffic. It is absolutely normal and at the same time it brings in a lot of sales and profit. But a good part of the branded traffic comes from people who were determined to search for Lego and their products anyway. Thus, branded traffic does not directly bring in new customers. Instead, the focus of SEO optimization should be on unbranded searches especially when you want to increase your market share relative to other competitors.
An example of a brand that gets a lot non-branded traffic is ikea.com:

Ikea gets 5.1 million organic traffic from non-branded queries in the US, with a total organic traffic of 173 million:

Problem 2: Missing opportunities for branded searches
Informational articles published on their website
On the other hand, big brands miss huge opportunities to capture more organic traffic and even profitability from branded searches.
For example, there are keywords which are not targeted by Lego, but targeted very well by smaller websites. For example: “most expensive lego set”

Certainly the existence of these items on the smaller sites may also end up in one form or another bringing revenue to Lego, but most likely at a much lower profitability as the smaller sites promote websites they are affiliated with such as Amazon and eBay:

In this case, Lego has an affiliate program and has been included among the purchase options, which is a very good thing.
Of course that the costs are also important when thinking about a strategy to get organic results, but as we can see in the screenshot, the article published by brickeconomy.com generates 13.5 thousand visits per month from search engines alone.
Considering that the conversion rate for an article of this kind can be between 0.5% and 1% (source), let’s assume that this article will have a conversion rate of 0.1%, just to be very pessimistic. Assuming an average order value of 500 euros (because that’s how much the products on that page cost), calculating it, we get:
Monthly income: 6,750 euro
Income per year: 81,000 euro
These revenues would be generated only from one blog article.
Product pages and category pages
Even for product or category pages organic traffic is lost, with other sites appearing at the top such as Amazon. To be clear, the name of the site is a very important criterion for Google searches. This means that when someone searches for a brand name, they will be favoured to a certain extent by the site that belongs to the brand. Therefore, it wouldn’t have been difficult for Lego to rank #1 for these keywords.
Of course there are products that may not exist, such as “lego pokemon”, but one can also use the information gained from keyword and competition research to bring new products to the site.

Problem 3: Informational articles are not SEO optimized
There are many SEO optimizations missing for articles published on lego.cum, and this is best seen when looking at the organic traffic obtained compared to their competitors.
To make it even clearer, high authority sites have the opportunity to appear on Google among the top positions almost instantly. However, this also depends on the content they publish and their SEO optimizations, such as understanding search intent, creating valuable content, etc.
For example, this article from lego.com generates 123 organic visits per month:

At the same time, an article published by another site, targeting the same main keywords generates 5.8 thousand organic visits:

Note: the 5.8 thousand organic visits are estimated for May 2023, being an article that has a high seasonality, September-December being the months that generate the most traffic for this article.
Problem 4: Category pages don't rank high on Google and don't generate much organic traffic
There are highly searched keywords for which Lego already has dedicated pages, but they don’t generate much organic traffic.
Example:

Although the keyword has a search volume of 33.1 thousand in the US alone, Lego gets only 49 organic visits for this keyword, ranking 26th.

If from the total of 100 thousand organic searches for the keyword “dinosaur toys” Lego managed to get 10 thousand organic visits, at a conversion rate of 1% (the conversion rate is usually higher for product/category pages compared to informational articles) and an average order value of only €50, they would generate annual revenues of €60,000 from this page alone.
Ikea shows another good example, ranking at the top of Google even for the most general words such as “sofa”, “armchair” or “bed frame”.
