Why is so much focus put on the Dow Jones Industrial Average?

IMO:

1. Tradition: people have been following it for a Really Long Time.
2. Laziness: do media outlets want to put the effort into finding something better.
3. Practicality: a lot of people are invested in the stock market.

EDIT: 4. "The Dow" is easier to say, and more dramatic, than "the S&P 500" or "the NASDAQ".

I think that you've been sidetracked by a number of factors such as price weighted versus capitalization weighted, the Dow Divisor as a multiplier, and the exchange that the stocks trade on. In addition, if you're interested in a large cap versus small cap comparison then compare indexes representative of those sectors.

The DJIA and other indexes are a reflection of the stock market. They are not are not an indicator of the health of the US economy.

As for why the DJIA is so widely followed, it might be because it's the second oldest US stock market index. It may just be force of habit. Over the past 5, 10 and 20 years, the S&P 500 has outperformed the DJIA or vice versa by less than one percent so despite the DJIA being composed of only 30 stocks, it has been a fairly good indicator of the overall stock market.

The DJIA is followed by non-investors, and even by investors who are only invested through their 401(k) or a mutual fund in their IRA. It is reported during the quick market updates given on news radio, and local TV news. It is in heavy rotation on the lower third chyron on cable news.

But why? Because it is easy to "understand": going up is good, going down is bad. But there are other US and global indexes that could do the same thing, so why not one of those? 30 stocks are easy to understand. Almost all of them are recognizable to non-investors.

Yes you can explain why others are better indicators, but to most people those are not important reasons. Those are technical reasons that they don't care about. The Dow-Jones Industrial Average is what they know. The biggest reason why they should care about the S&P500 is that the performance of their 401(k) and IRA investments are compared with that index. But still they evaluate health of the economy with the DJIA.

Equating any stock index as an indicator of the US economy is problematic. We are currently in a global pandemic where the unemployment rate is going up, the number of people using food banks is going up, hospitals are full; but the market just hit a new record - therefore the economy is great.

The DJIA is the only common stock index composed of stocks that have been carefully chosen to represent the range of industries that make up the economy. Most other indexes are composed of stocks chosen using relatively simple algorithms: the S&P 500 is the top 500 US public companies by market capitalization, the NASDAQ Composite Index is all companies that trade on the NASDAQ exchange.

The 30 companies in the Dow Jones, on the other hand, have been chosen to be most representative of their respective industries. And the composition of this group is changed over time to reflect how important various industries are in the US economy.

While there's some subjectivity to this selection, and even possibly some form of self-fulfilling prophecy (adding a company to the DJIA may attract investors to it), historically the DJIA has correlated pretty well with the market as a whole. And it can be easier to understand why it moves as it does, because there are so few variables involved.

It can be instructive to look at how the composition of the Dow 30 has changed. The current index is heavy in information tehnology (Apple, Microsoft, IBM, Intel, Salesforce, Cisco), financial services (Visa, Goldman Sachs, JPMorgan Chase, AmEx), health care, and retailing (although the retail sector is still all brick&mortar chains -- it can't be too long before Amazon.com joins). Many years go there was a much larger emphasis on industrial machinery and agriculture because those were much more important sectors of the US economy. General Electric was in the index since its inception (over a century), but was replaced in 2018 as they had been struggling to find their place in the 21st century economy, even though they're still an enormous company.