Washers are a relative rarity in New York; the New York Times in 2011 asserted them as "Manhattan Status Symbols" and quotes only 20% of apartments in the city having one.

The comparison with Tokyo is in fact a great one, as it does make a good rough analogue for New York City yet has more washing machines, quite simply because: New York City buildings are on average, quite old at roughly 90 years, whereas Tokyo's average is 26. In Japan generally, a Ministry of Land, Infrastructure, and Transport report in 2013 found only 10,000 buildings built before 1963 (out of ~1.3 million).

Tokyo was razed with firebombs during WWII and the Japanese financial system and culture have housing that depreciates (the value is in the land, not the building). The tax structure set after WWII encouraged a destroy-and-rebuild structure, and frequent earthquakes and consequent building code updates led to even more encouragement (changing a building's earthquake specs being a quite expensive endeavor, making it easier to just demolish and start over).

For some perspective, changes to the earthquake code happened in 1924 (minimum thickness for wooden beams, reinforced concrete requiring braces), 1950 (load bearing walls, extra framework for wooden structures), 1971 (wooden structures need reinforced concrete), 1981 (an upping of magnitude resistance after the 1978 Miyagi Earthquake which was at 7.4), and 2000 (regulations requiring testing braces, foundations, and beams of a structure).

New York had no such issue. They did have massive amounts of immigration (due to both being a port entry-point, and being a center of manufacture) causing a large building boom in the 1900-1920 without nearly as much a culture of demolish-and-rebuild. (Their big code updates tended to happen because of fire, not earthquakes; not as fundamental a building change needed.)

So why is the age so important? "Modern" washing machines really only became a breakout product in the 1950s (also when laundromats started getting big), evidenced by the utility fixture building codes in NYC not arising until the early 1950s (the prior 1938 codes did not have such provisions). The amendments specifically related to cooking and drying, which used gas, so there were amendments such as (for example) cutoff valves for higher pressure gas requiring regular inspection. Washing machines and dryers received water-resistant outlet requirements. This means the average building in New York was built before any utility regulations so at the very least a washing machine would require, say, a new outlet. For modern code, there needs to be large space for drainage -- and plumbing is expensive.

Hence, the transition to personal washing machines has been quite slow. The 1970s did see one new development with the apartment laundry room:

In many new apartment designs the laundry room is likely to accompany a solarium, patio, lounge or swimming pool, or a play area for children. Even when it is placed in the basement, the traditional spot, the trend is to place laundry facilities behind a large window or at least in view of the elevator, for safety's sake, or to carve out earth around a basement to let in light.

This was not enough to make an immediate dent in the number of laundromats. However, in areas where higher-rent buildings with apartment laundry rooms are common, laundromats are starting to reduce in number; this means (in addition to a certain pandemic too recent to discuss here) the laundromat is not being killed off not so much by the personal washing machine but the in-building one.

...

Koo, R., & Sasaki, M. (2008). Obstacles to affluence: thoughts on Japanese housing. NRI Papers, 137(12), 1-14.

Spivack, D. (2016). Amending the Building Code in New York City: Exploring Forces that Influenced Change. New Jersey Institute of Technology, Dissertation.

Waswo, A. (2002). Housing in Postwar Japan: A Social History. Routledge: Psychology Press.

No discussion of washing machines and laundromats should go by without at least a mention of the prevalence of wash-and-fold service, particularly the Chinese hand laundry industry, which was discussed by u/GSpess in this response.

Beyond the economic, legal, and engineering limitations to the widespread installation of washing machines in New York apartments that are laid out by u/jbdyer, there is the also the robust tradition of commercial laundry services staffed by immigrants in urban areas throughout North America. Many of those in the middle and upper-middle classes who lived in apartments would send laundry out, as it was less time-consuming, cheaper, and often guaranteed a more thorough result.

This changed somewhat with the widespread adoption of washers and dryers and the development of the laundromat in the post-World War II era. The acceptance of the washing machine owes much to the expansion of postwar suburbia, as more and more Americans occupied their own single-family homes in homogeneous, low-density communities. But the tradition of wash-and-fold service (now supplemented with dry cleaning) has been long to die—partly due to habit and partly to convenience.

Serenity now, new and old friends, serenity now!

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