The short answer? When Major League Soccer (MLS) was founded in the aftermath of the 1994 FIFA World Cup, (FIFA states that in order to host a World Cup, you must have a national professional league. They gave the United States an exemption, with the contingency that a league would be formed after the tournament.) the league was founded as a Single Entity, meaning that teams were not individually owned. All teams are owned by the league, with individual investor/operators (the owners) who handle specific franchises. That being said, this specific topic has come under the microscope in recent years.
As we just covered, MLS is set up different than most other sports leagues. Because of the single entity structure and "franchises," instead of Football Clubs (like the rest of the world), owners buy into MLS, not into an American Soccer System that promotes or demotes teams into tiers. The United States Soccer Federation (USSF) is the United States' FIFA representative organization, and decided that not only are they fine with no promotion/relegation, but officially ruled that MLS is the top soccer league in the United States.
Just because Major League Soccer is the top league in the United States does not mean that there are not lower division soccer clubs that exist. In fact, in 2018, the United Soccer League (USL) has been given a Division II status by the USSF, one division below MLS. The USL is comprised of 33 clubs, many with an affiliation to an MLS franchise. This affiliation allows the MLS to loan players to the designated USL team.
Prior to 2018, the North American Soccer League (NASL) had operated since 2011 as another Division II league, only to cancel their 2018 campaign after filing legal action against the USSF.
There are two separate litigations that could dramatically impact this entire topic moving forward. The first is the previously mentioned antitrust lawsuit brought against the USSF by the NASL. The NASL fell below the minimum teams required for divisional status according to the USSF rules. When the USSF removed all division status from NASL, the latter filed the litigation, arguing that there should be no divisions in the United States.
A separate, yet related case against the USSF has been filed by two lower level clubs. Miami FC (NASL) and Stockade FC (National Premier Soccer League) have filed a case with the Court of Arbitration for Sport in Switzerland. This court handles sporting specific issues with many organizations, but the most pertinent to this discussion is FIFA. The club's argue that the USSF is in violation of the FIFA rules, specifically, in qualification for the World Cup. FIFA rules state that for a nation to be eligible for a World Cup, that nation's domestic league must enforce promotion relegation. (Under Article 9, Page 73)
While neither case has been resolved, the current status quo is being challenged. Whether this results in promotion/relegation remains to be seen.
Major League Soccer (MLS) has never adopted promotion and relegation and the United States Soccer Federation (USSF) has never ordered them to implement it. The USSF could rule that Major League Soccer has to adopt promotion and relegation to be officially deemed the top league in the United States, but at this juncture, MLS has far more resources than any other league, any lack of designation would have little impact.
Rather, USSF has decided that assisting MLS as currently constructed is the best course of action for the growth and health of soccer in the United States.
However, there is a pending case that could impact all of this.
All of this may change. As we talked about more in depth in another question, there is currently a pending case with the Court for Arbitration for Sport (CAS) in Switzerland that could impact the USSF's decision to continue without promotion and relegation.
Miami FC (NASL) and Stockade FC (National Premier Soccer League) have filed a case with the CAS over promotion and relegation. This court handles sporting specific issues with many organizations, but the most pertinent to this discussion is FIFA. The club's argue that the USSF is in violation of the FIFA rules, specifically, in qualification for the World Cup. FIFA rules state that for a nation to be eligible for a World Cup, that nation's domestic league must enforce promotion relegation. (Under Article 9, Page 73) We likely won't know for some time the outcome of this case.