To answer your question briefly: net income is affected by many things inside and outside of management control, and must be supplemented by other elements to gain a clear picture of a company's health.
To answer your question in-depth, we must look at the history of financial reporting:
Initially, accounting was primarily cash-based. That is, a business records a sale when a customer pays them cash, and records expenses when cash goes out the door. This was not a perfectly accurate system, as cashflow might be quite erratic even if sales are stable (collection times may differ, etc.).
To combat problems with cash-based accounting, financial reporting moved to an accrual-based system. An accrual is the recording of an item before it has fully completed in a cash transaction. For example, when you ship goods to a customer and they owe you money, you record the revenue - then you record the future collection of cash as a balance sheet item, rather than an income statement item. Another example: if your landlord charges you rent on December 31st for the past year, then in each month leading up to December, you accrue the expense on the income statement, even though you haven't paid the landlord yet.
Accrual-based accounting leaves room for accounting manipulation. Enron is a prime example; among other things, they were accruing revenue for sales that had not occurred. This 'accelerated' their income, by having it recorded years before cash was ever collectible. There are specific guidelines that restrict doing things like this, but management will still attempt to accelerate net income as much as possible under accounting guidelines. Public companies have their financial statements audited by unrelated accounting firms - theoretically, they exist to catch material misstatements in the financial statements.
Finally, some items impacting profit do not show up in net income - they show up in "Other Comprehensive Income" (OCI). OCI is meant to show items that occurred in the year, but were outside of management control. For example, changes in the value of foreign subsidiaries, due to fluctuations in currency exchange rates. Or changes in the value of company pension plan, which are impacted by the stock market. However, while OCI is meant to pick up all non-management-caused items, it is a grey area and may not be 100% representative of this idea.
So in theory, net income is meant to represent items within management control. However, given the grey area in accounting interpretation, net income may be 'accelerated', and it also may include some items that occurred by some 'random business fluke' outside of company control.
Finally, consider that financial statements are prepared months after the last year-end. So a company may show great profit for 2015 when statements come out in March, but perhaps Jan-March results are terrible.
In conclusion, net income is an attempt at giving what you want: an accurate representation of the health of a company in terms of what is under management control. However it may be inaccurate due to various factors, from malfeasance to incompetence.
That's why other financial measures exist - as another way to answer the same question about a company's health, to see if those answers agree. ex: Say net income is $10M this year, but was only $6M last year - great, it went up by $4M! But now assume that Accounts Receivable shows $7M owed to the company at Dec 31, when last year there was only $1M owed to the company. That might imply that there are problems collecting on that additional revenue (perhaps revenue was recorded prematurely, or perhaps they sold to customers who went bankrupt).
Unfortunately there is no single number that you can use to see the whole company - different metrics must be used in conjunction to get a clear picture.