There are various things profit (or loss) is not.
It is not simply return to risk. All incomes have an element of return to risk. Interest on loans, most obviously, but also rents of land, various forms of wages. One reason why males earn more than females on average even for full-time work is males tend to do more dangerous jobs (hence their markedly higher rate of death and serious injury at work) and so earn a risk premium.
It is not simply return to capital. Providing capital to a firm does not make one an owner. Bondholders are not shareholders. There are other forms of return to capital (most obviously interest on loans) than ownership.
It is not return to coordination. That is what managers (and other employees) do. Many owners are also managers of their business but many more are not. Indeed, it is notorious in modern corporate governance that there is a principal-agent problem in hiring, firing and paying managers. But that extends all the way down a corporation. Corporations typically pay better than small firms because, in a large corporation, it is hard (or even impossible) to ascertain the connection of the efforts of any particular employee to net income. So—given corporations can spread risk more easily than small firms—they pay a premium to employees to encourage their employees to self-police in order to keep those extra benefits. In effect, this premium is a hostage for good behaviour. Of course, how well this “hostage-premium” is managed will vary from corporation to corporation or part thereof.
Returning to ownership and net income, let us consider that “bearing the loss” part again. What sort of person covers losses? A guarantor.
A firm has various expenses in production, distribution and sales. It hopes that its revenue will more than cover its expenses. But, if they do not, someone has to be the guarantor of that income shortfall. That is the owner. So, as Yoram Barzel explains in his Economic Analysis of Property Rights, the owner of a firm is the guarantor of such income variability: hence the boundaries of the firm are determined by the scope of the guarantee by the equity capital. (This post is a working through of Barzel’s analysis, as I understand it.)
Why is said ownership purchased? Because the owner is the guarantor of income variability and such a guarantee requires capital. The capital put up is the size of the guarantee. So the share of the ownership is the share of the guarantee purchased.
In the case of "sweat equity", one is foregoing full return on one’s labour in order to build up the value of the firm. But that value is then the basis for the guarantee against income variability.
The owner, as the guarantor against income variability, thus receives the residuum – the variable net income of the firm: the profit or loss made by the firm after all other claimants on the firm’s income have been paid. Hence the residuum being the return to ownership, given not all capital is owner-capital. Profit is what one gets for covering the risk of loss.*
Folk obviously prefer to get as much profit as possible for as little risk of loss as possible. Hence any belief that there is a "one-way bet" in asset values—for example, because officials restrict the use of land for housing, a restricting of quantity response to demand leading to a bigger price response due to regulation increasing scarcity—naturally leads to asset bubbles by adding the demand for an inflation-beating asset to the demand for the normal use of the asset.
If profit is what one gets for covering the risk of loss, then profit comes from
Since the owner is providing the final guarantee, they are also the final authority in the company. Thereby connecting guarantee with control. To provide a guarantee without any control is clearly a highly risky action. (Ask US taxpayers after the Savings & Loans and Freddie Mac/Fannie Mae debacles where they did not even have the indirect control that government ownership offers.) Hence companies provide dividends, offer capital growth—forms of return on the guarantee—and give shareholders the right to elect the directors and the ability to exit as owners—forms of control over what is being guaranteed. It is in this—somewhat removed or indirect—sense that the share market is the market for managerial control.
Conversely, having control without owning the capital at stake provides poor incentives to protect the value of the capital or to use it efficiently. The notorious tendency of government-owned enterprises towards declining productivity can largely be traced to this. (The rest of said tendency comes from the conflict of interest in the same authority being regulator and producer, a conflict that is particularly intense if not ameliorated by democratic accountability—hence the appalling environmental protection record of the command economies: the rulers-as-regulators having somewhat limited interest in restricting their own behaviour as producers.**)
So, purchasing ownership is purchasing that final authority (whether a tiny bit, a more substantial bit or all of it). And matching final authority with being guarantor means aligning final say with final risk with final return. Hence that authority having the final responsibility for who ultimately coordinates. Hence ownership is purchased and receiver of the net income of the firm.
* Return to scarcity—particularly scarcity due to regulatory privilege (statutory monopolies and other barriers to entry) or regulatory barriers (smuggling, black markets)—can be earned as supernormal profit. Not that either is without risks.
** Even if there is democratic accountability (an instrument of highly erratic and variable effectiveness), that does not abolish the problem. The persistent problems of school performance are a natural outcome of the main regulator being the producer. Everyone can see it would be obviously a stupid way to run a sporting code to have the most powerful club also appoint the umpires and set the rules. That is, however, apparently a fine way to educate children: apparently on the grounds that education ministers and bureaucrats are magically immune to the obvious conflict of interest. Democratic accountability has value, but it is not so effective that it wipes out the conflict of interest involved in having a producer (in the case of schools, the biggest producer, so with the most to be embarrassed/constrained by) set and enforce the rules.