Three to start with: public education, prison systems, and health care.
Do I need to go into details on this? Okay, here goes.
Health care: companies that are in business, any business, to make a profit, need to maximize income, and minimize outflow. This means that a for-profit insurance company needs to get premiums as high as they can get away with, and pay out as little benefits as possible. In "regular" businesses, this can be bad; price-gouging, monopolies, and so on. In health care, when benefits are minimal, people die. Or at least, lose their homes and go bankrupt trying to pay for necessary, even life-saving, treatments. It has happened already, and often. Being a for-profit company, even if it's not in the name or description, but only in the goals of the leadership, requires putting money income above all else. In health insurance, that means money above human health and lives. Insurance companies have even rebranded their wares as "insurance products." Is that what we want for an insurance provider?
Prisons: this one's even easier. Prisons for profit makes prisoners money earnings. More prisoners means more profit, fewer prisoners means less profit. Prisons run by profit-driven companies can have no interest in preventing crimes from happening, stopping recidivism, or common-sense altering of sentencing (lighter sentences for first-timers, rehab instead of prison for drug addicts, etc.), because prisoners are profit centers; all of those lower profits and must be fought with any and all legal methods (even quasi-legal) available. Getting "career criminals" on an honest track, treating drug-addiction as medical and treating it for healing, common-sense precautions to prevent criminal behavior, all of these will reduce profits and cannot be tolerated.
Public education: okay, this one's really important to me. Remember, I'm a schoolteacher. Actually, it's kind of the same reason as health care, above. Many companies are trying to get into public education and standardized testing right now. This testing, when done right, can in fact inform instruction and increase the effectiveness of teaching. WHEN DONE RIGHT. I'm not convinced that these new tests and testing systems are being done right, and many many parents aren't either. Just look at the growing "opt-out" movement in states with the new standards and the reasons given for them. The questions are haphazard, some aren't even grade-level appropriate, the data isn't returned for months, sometimes not until the next school year; far too long to be effective in modifying instruction. And with some of the companies, the scores that are returned are a single value, with no details or even insight into the methods of the scoring. Complete opacity of the scoring. These companies genuinely seem to be interested in selling tests and testing materials and methods, not for helping instruction, but for the profits to be generated from the testing products, and possible extra profits generated from "remediation" programs because the students did poorly on the tests (according to the company who wants to sell the remediation). As with prisoners, above, students are seen as profit centers, not really even thought of by the companies as people, just an income source.
I do feel that I must mention that, since my district does in fact use the new standardized testing, of course I will proctor the tests as needed by the district administration, and I will not actively attempt to convince any student to opt out of the testing. I'll ride this out, and whatever next "new and improved" thing follows this, and do my best to help my students kindle a love of learning, and developing skills that are not limited to picking a multiple-choice answer. With what instructional time remains during the school year.
So, there it is. Even in modern capitalist America, some things really shouldn't be done expressly for profit. If the company does profit from its efforts in any of the above areas, then they're a financial success, and they deserve success. But if a company is entering these fields only because the projected earning potential, then nothing in those areas will be improved. Health care outcomes will still be among the worst in the developed world, prisons will be the largest percentage of the population in the developed world, and the public education system will still be broken, and used as a whipping post for politicians, and the students will continue to suffer mediocre outcomes and lack of thinking skills and problem solving ability.
And, worst of all, with companies profiting from these areas, they will be able to use their earnings to control the political climate, and no reforms that actually benefit people and society will be permitted to succeed.