Why do firms with more-diverse shareholder bases often pay higher dividends than private firms or public firms?
This is a question of the chicken and the egg. Most likely companies have pay out good dividends attract shareholders, who are looking for both stock appreciation and dividend payments and not the other way around. In light of this, it is just the reverse of the logic or your question.
There are a few important points to be made.
First, people like dividends, because there is a regular stream of money that they receive in addition to stock appreciation. More importantly, dividends are only taxed at 15%, which is excellent in view of what it could be.
Second, many pensions and other types of large funds only invest in companies that pay dividends. This means that when a company pays handsome dividends, more institutional investors will flock to it. For example, once the company, Apple, stated that the would issue dividends, many institutional investors were interested.
In conclusion, a diversity of people invest in companies with consistent and high yielding dividends.