Actually, share holder value is is better maximised by borrowing, and paying dividends is fairly irrelevant but a natural phase on a mature and stable company.
Company finance is generally a balance between borrowing, and money raised from shares. It should be self evident with a little thought that if not now, then in the future, a company should be able to create earnings in excess of the cost of borrowing, or it's not a very valuable company to invest in! In fact what's the point of borrowing if the cost of the interest is greater than whatever wealth is being generated? The important thing about this is that money raised from shares is more expensive than borrowing.
If a company doesn't pay dividends, and its share price goes up because of the increasing value of the business, and in your example the company is not borrowing more because of this, then the proportion of the value of the company that is based on the borrowing goes down. So, this means a higher and higher proportion of the finance of a company is provided by the more expensive share holders than the less expensive borrowing, and thus the company is actually providing LESS value to share holders than it might.
Of course, if a company doesn't pay a dividend AND borrows more, this is not true, but that's not the scenario in your question, and generally mature companies with mature earnings may as well pay dividends as they aren't on a massive expansion drive in the same way.
Now, this relative expense of share holders and borrowing is MORE true for a mature company with stable earnings, as they are less of a risk and can borrow at more favourable rates, AND such a company is LIKELY to be expanding less rapidly than a small new innovative company, so for both these reasons returning money to share holders and borrowing (or maintaining existing lending facilities) maintains a relatively more efficient financing ratio.
Of course all this means that in theory, a company should be more efficient if it has no share holders at all and borrows ALL of the money it needs. Yes. In practise though, lenders aren't so keen on that scenario, they would rather have shareholders sharing the risk, and lending a less than 100% proportion of the total of a companies finance means they are much more likely to get their money back if things go horribly wrong.
To take a small start up company by comparison, lenders will be leary of lending at all, and will certainly impose high rates if they do, or ask for guarantors, or demand security (and security is only available if there is other investment besides the loan). So this is why a small start up is likely to be much more heavily or exclusively funded by share holders.
Also the start up is likely not to pay a dividend, because for a start it's probably not making any profit, but even if it is and could pay a dividend, in this situation borrowing is unavailable or very expensive and this is a rapidly growing business that wants to keep its hands on all the cash it can to accelerate itself.
Once it starts making money of course a start up is on its way to making the transition, it becomes able to borrow money at sensible rates, it becomes bigger and more valuable on the back of the borrowing.
Another important point is that dividend income is more stable, at least for the mature companies with stable earnings of your scenario, and investors like stability. If all the income from a portfolio has to be generated by sales, what happens when there is a market crash? Suddenly the investor has to pay, where as with dividends, the company pays, at least for a while. If a company's earnings are hit by market conditions of course it's likely the dividend will eventually be cut, but short term volatility should be largely eliminated.