Promotion/relegation isn't restricted to football in Europe. It works in all sports: basketball, volleyball, handball, rugby, field hockey... So the size of the market isn't really what makes it valid or not. It's really a culture.
Kind of? It comes down to how teams are oriented. In the US sports teams are private entities owned and operated by individuals or small groups of individuals. It's their thing. To do with as they see fit. There's a wider league body which handles league operations, and this is overseen by a commissioner, but the commissioner more or less acts at the behest of the group of owners whom comprise the league, and therefore anything the commissioner is doing is done to the benefit of the owners and nobody else. This relationship has created a rather different relationship between team and fan in the US. For all the BS owners and community organizers throw out about how everything is done for the fans and the power of the 12th Man or whatever, fans are regarded more or less as 3rd party observers. The league and its operations are an "owners and players" Thing and you fans should consider yourself so lucky that you get to watch it. Owners/GMs are free to bring in and discard whoever they want, build and tear down whatever stadia they feel like, and even pack the team up and move to the other side of the country, if it should please them. This is in stark contrast to the European Club system, where the club was for a long time (and in many clubs still are to a decent extent) owned by the city/its supporters collectively. The club is regarded as an intrinsic part of the city and to move Chelsea out of London or Barcelona out of Barcelona would be unconscionable. Just look at what Cardiff City supporters did for the mere sleight of altering the crest and colors of the team. Redesigns happen all the time in American sports. Two of the biggest, most successful baseball teams in the largest city in the country packed up and moved across the country, virtually without warning at the height of their success. It seems unthinkable that the Yankees would ever move out of New York, but that's the sort of thing we're talking about here. It's not that uncommon in American sports.
Now sure. At this point that is very much a cultural Thing. But it's also a rather interesting historical point, and serves as a useful counterfactual to how things could conceivably have played out in European Soccer. In the 1860s, much like with England's Football Association, Baseball had a large overseeing body NABBP (National Association of Base Ball Players). Much like Soccer Baseball had a controversy in the late 1860s/70s over the question of professionality in baseball. Just like with the FA the result was the group splitting in two: the NABBP (for Amateur leagues) and the NA (for Professional). Unlike the FA the NA collapsed under its own weight and inability to regulate the league. Power became concentrated in a select group of teams and the power dynamic from the outset of professional baseball was wealthy individuals employing and controlling players. With the collapse of the NA leagues broke down into scattered regional leagues. The most wealthy and powerful owners banded together to form the National League, which also happened to sit in the largest, wealthiest cities on the East Coast and Midwest: New York, Boston, Chicago, Philadelphia, St. Louis, Pittsburgh, Baltimore, Cleveland, etc. As the owners called the shots it was therefore in their mutual interest to regulate their product. Unlike an organization like the FA, which is acting on the best interests of the entirety of Association Football as a sport, the National League was operating on the best interests of the league in question. Ensuring that the product was competitive and either cutting out (as in the case, for example, of the upstart Players League, the Federal League, the Pacific Coast League) or integrating (as with the American League) competitors as they saw fit. In the example of baseball particularly, there were "lower leagues" as you have in soccer, but those lower leagues were ruthlessly annihilated in the 19teens and 20s, and later bought and incorporated into a vertically integrated monopoly operating to the benefit of the individual team that bought them. Baseball's example set the precedent for all future professional sports leagues in the country - owners forming a tightly knit, and tightly regulated organization operating for their personal benefit. Competitors are either destroyed or incorporated into the existing system (both the NFL and NBA had situations similar to the NL where competing leagues were brought into the fold (the AFL, ABA, and AL respectively). It's certainly conceivable, had the National Association not folded, that baseball could have adopted a tiered pro/rel system similar to Soccer.
Personally I think pro/rel is more interesting to watch. But due to the way leagues are oriented - enterprises existing to enrich the owner (rather than fans, the league, the sport, or anything else) - they simply are never going to arrive at a system whereby an owner could risk being ousted through no fault of their own.
That being said the American system certainly has its own benefits. As much as I like the pro/rel system conceptually the results in actuality are kind of garbage. In the four major European soccer leagues you effectively have a severe stratification of teams. BPL has Chelsea, ManU, ManCity (admittedly a more recent admission), Arsenal, Liverpool, and Tottenham (once in awhile) seriously competing for titles at any one time. The same rota of 6 or 7 teams are altering between Premier and Champion year in year out. Money dictates European soccer at a level that it REALLY doesn't in American leagues. And because of that, and the MASSIVE gap between top flight and 2nd flight soccer you don't really see the same kind of long-term vision/cycle that you see in American sports. The 49ers and Seahawks went through a decade of gradual accumulation of talent through the draft and savvy trading before putting themselves on the top of the NFL. The Astros, Cubs, Padres, and Mets are now doing the same in baseball, reaping the rewards of the 5-6 years of planning, of carefully developing farm systems, and tradding at the right time. The Warriors and Cavaliers are in the NBA finals because of a combination of front office wizardry and enormous fortune. The Warriors haven't won a title since 1975, the Cavs have never won one. How often does that happen in the BPL? Could you ever see Leicester City or Norwich or someone winning the premiership? European soccer is interesting to me because the league setup is so different, but there's such an air of inevitability about the whole thing that makes it kind of depressing to watch. La Liga is just a competition between Barça and Real year in and year out. Bayern won the Bundesliga by 10 points, and last year they won it by 19. Arsenal, Chelsea, ManU, and Liverpool together haven't been relegated in over 30 years, and if you cut out Chelsea it's twice that stretch. Sure there are more things to watch for - Champions League berths, Europa League berths, pro/rel - but money rules things in soccer like they do in no American league.
Perhaps that's why Americans are obsessed with championships in a way European sports fans aren't - because they're that much more of a likelihood for any given team in the US.