Caveats
First, there really isn't such a thing as a "for profit" limited liability company. There are merely "limited liability companies" in general. Under the laws of most states, including New York, a limited liability company can be operated for either "for profit" or "non-profit" activities, so long as they are lawful activities.
For what it is worth, I have some experience with people trying to organize a primary non-profit entity (an HOA) in limited liability company form (as opposed to using an LLC subsidiary for a different primary non-profit entity). I would strongly discourage anyone from trying to organize a primary non-profit entity in that form, as the limited liability company form is very ill-suited to being a non-profit in its own right for a variety of reasons beyond the scope of this question. But, in theory, it can be done.
Second, the law of unrelated business income taxation is set forth primarily at 26 U.S.C. §§ 501, 502, 503, 512 and 513 and in the related regulations. It is quite byzantine, and has many special rules and exceptions. The explanation below oversimplifies the situation to cover the "typical" case and the issues the question seems to be concerned about. A variety of statistics about unrelated business income, and IRS publications explaining it, can be found at the relevant portion of the IRS website.
Analysis
A 501(c)(3) that 100% owns a limited liability company, like any domestic entity or domestic person, who owns 100% of a limited liability company, can elect that it be taxed one of two ways under the "check the box" regulations of the IRS that were effective January 1, 1997. See Treasury Regulations §§ 301.7701-1 through 301.7701-3.
One way is to elect that the limited liability company will be treated for income tax purposes as a disregarded entity. This would typically be done in the case of a passive investment asset, like rental real estate or a lease of the ground upon which a skyscraper is built, that does not trigger unrelated business income treatment, in order to insulate the other assets of the non-profit from liability arising from that passive investment asset.
The other way is to elect that the limited liability company will be taxed as a corporation.
Many limited liability companies taxed as a corporation that are owned by private individuals further elect that it be taxed as an S-corporation, but that option is not a good option for a non-profit, for which S-corporation income is per se unrelated business income for the non-profit.
Shares in a C-corporation are, generally speaking, treated as a passive investment, and dividends from those shares are generally not unrelated business income (and are not taxable income to a 501(c)(3) due to its tax exemption). But, the corporate level income tax imposed a C-corporation profits is equivalent in amount to the unrelated business income tax imposed on non-profits with unrelated business income in the same amount as the profits from the C-corporation.
C-corporation taxation is still the only sensible choice, however, for income that in not a passive investment for a non-profit corporation, because there are two downsides to a non-profit to having unrelated business income. One is the tax, equivalent to C-corporation income taxes, that applies to unrelated business income. The other is that if a non-profit has too much unrelated business income, the non-profit's status as a 501(c)(3) entity is terminated.
If a non-profit, instead, puts activities that would otherwise be considered unrelated business income in a limited liability company that elected to be taxed as a C-corporation, or simply puts it in a C-corporation that is organized under state law as a corporation, its status as a non-profit is not impaired.
So, a non-profit that is a 100% owner of an LLC, doesn't get any more favorable treatment with respect to unrelated business income restrictions that it could have at any time since the unrelated business income tax was invented in 1950 using a C-corporation subsidary. As the official IRS history of non-profit taxation explains:
Before the 1950s, tax-exempt organizations could earn tax-free income
from both mission-related activities and commercial business
activities that were unrelated to the purpose for which they were
exempt, as long as they used the net profits for exempt purposes.
However, in the 1940s, concerns grew in Congress over the perception
that tax-exempt organizations were permitted an unfair competitive
advantage over taxable entities. As a result, Congress established the
“unrelated business income tax” (UBIT) as part of the Revenue Act of
1950. For tax years beginning after December 31, 1950, UBIT was imposed on the “unrelated business income” (UBI) of charitable
organizations (except churches); labor and agricultural organizations;
chambers of commerce, business leagues, and real estate boards;
certain trusts; and certain title holding companies.
Income was considered UBI if it was produced from an activity deemed a
“trade or business” that was “regularly carried on” and was not
“substantially related” to the organization’s exempt purpose(s),
regardless of whether or not the profits from the unrelated trade or
business were used solely for exempt purposes. Passive income and
certain gains and losses from the disposition of property were not
subject to tax.
The Revenue Act of 1950 addressed several other issues regarding the
unrelated activities of tax exempt organizations. Tax exemption was no
longer permitted to “feeder” organizations, which did not conduct any
charitable activities, but rather operated commercial enterprises from
which they passed income to a charitable organization. In addition,
income from debt-financed real estate sale-leaseback activities was
subject to UBIT. In these cases, tax-exempt organizations purchased
real estate with borrowed funds, leased the property back to the
owner, and used the tax-free rental income to pay off the debt.
The Revenue Act of 1950, and additional changes made under the Tax
Reform Act of 1969, discussed in the following section, formed the
contemporary structure for the unrelated business taxation of
tax-exempt organizations.
At that time, corporations were taxed at a 23% tax rate on their first $25,000 and a 42% tax rate on any further income (except long term capital gains for assets held more than six months which were taxed at a 25% rate), and an excess profits tax was also in place from July 1950 through Calendar Year 1953. The excess profits tax was 30 percent of an adjusted profits figure reduced by credits for the level of prewar profits. It was not offset against income tax, but the sum of income and excess profits taxes was capped at a given percentage of income (from 62 percent to 70 percent).
In contrast, since January 1, 2018, all C-corporation income, and all unrelated business income of a non-profit corporation, has been taxed at a flat 21% federal income tax rate at the corporate level.
