Shareholders own a public company, so why shouldn't all of a company's income be distributed back to them? Why are dividends (if any) just a small fraction of a company's retained earnings?
As a shareholder in a public company, you typically want your investment to grow. Companies retain their earnings when they want, or need, to reinvest into their business. New products, acquisitions, market expansion, etc all require money so it typically makes sense to use excess earnings to fund these efforts.
If you're an investor that is only interested in dividend payments then you will typically only look to invest in companies that have a high dividend payout ratio, history of payments as well as their industry. For example, technology companies are growth oriented so they typically do not pay dividends as they need to fund their growth.
There's a lot more details on retained earnings here: Investopedia Details
Consider a highly simplified case.
Acme, Inc., is a successful company that produces and sells thromblemeisters to the general public. The company is split into 1,000,000 equal shares. Thromblemeisters are easy to make, there is little competition (maybe they have a patent on the technology), and the market is nowhere near saturated, so the only thing that affects the profit is how many that the company can sell, which in turn depends on how many they can make. (Another way of saying this is that the company's fixed costs are zero.)
The company was founded on January 1, 2018, immediately went public (no one said this was realistic, but really, public or not doesn't make a great deal of difference here) and hit the ground running; in the calendar year 2018, they made a profit of $100,000.
On January 1, 2019, the company has a choice to make. They can either take $90,000 of the $100,000 profit and invest it in expanding their production facilities, which will be enough to increase their production capacity by 50%, and separately choose whether or not to distribute the remaining $10,000 to the shareholders at $0.01 per share. Or, they can distribute all the profits to the shareholders at $0.10 per share, and maintain their current production capacity.
In the first case, profits in 2019 can be expected to be about 50% higher than they were in 2018, or about $150,000 per year. In the second case, profits in 2019 can be expected to be about the same as in 2018, or $100,000 per year.
In the second case, in its first two years the company makes $200,000 and, at the end of 2019, is left with $110,000 (minus up to $10,000 in dividends paid in 2018) in its bank accounts. It will keep making about $100,000 per year unless management changes their strategy.
In the first case, in its first two years the company makes $250,000 and, at the end of 2019, is left with $140,000 (minus up to $10,000 in dividends paid in 2018) in its bank accounts. It has the ability to scale production up further and still have a healthy bank account balance left. At this point, they can take another $90,000 to scale their production up by another ~30% (to twice what it was when they started), thus making $200,000 in 2020 alone, and still have some $40,000 to $50,000 in the bank. Even if they kept the dividend unchanged at $0.01 per share, they'll still have $30,000 in the bank going into 2020.
Now: Assuming that Acme Inc. is your company, which would you choose? Would you choose to have, at the end of the second year, $110,000 in the bank and flat (read: zero) growth, or $140,000 in the bank and significant growth?
In fairness, most cases are far from this simple, but it should be clear that keeping money within the company can be significantly more profitable than distributing it to shareholders as dividends, even before considering things like tax effects.
There are corporate structures that do require what you are asking about in some jurisdictions. In the United States, examples include:
REITs (Real estate investment trusts)
MLPs (master limited partnerships)
REITs are required to distribute at least 90% of their taxable income per year.
MLPs are required to distribute "all available cash" each year.
Otherwise, in a a general corporation you are reliant on the management as your agent to determine the distribution.
Although purchasing stock is colloquially said to represent part ownership of the business, in reality there are laws and contracts that delineate exactly what the shareholders are entitled to. Immediate payout of earnings is usually not part of these. So your conclusion that companies should distribute all of their earnings does not follow from your premise that shareholders "own a public company".
Using this model would make life much more complicated for investors, since ROI calculations would be more involved and there would presumably be more more trades (and commissions paid to brokers) as earnings are reinvested. This is probably part of why it is not common. Another part is that nobody else does it, and companies like to not be too crazy with their financing.
If you really wanted to, you could easily DIY a similar deal. Say you hold
s shares, every time an EPS of
e is announced, sell off about
s*e shares. This would incur fees, and you have to figure out what to do about negative earnings, but overall it should produce the same effect: In a company where value is driven by earnings, your cost basis will remain the same, while strong earnings will generate payouts for you.
Unfortunately, for many stocks, earnings do not determine price. They may go up despite low or negative earnings, or go down despite strong earnings. If it was the norm for earnings to be distributed, this means that share price would still be volatile due to those "other factors", perhaps even more so than now when it is balanced by earnings.