I'll take a stab at it.
Probably because when March rolls around there is a lot more warmer temps starting to enter the Southern US. In order to get an 18" snowstorm any time of the year you need a really strong, amped up/phasing situation. Or a really slow/almost stalling system so you get the proper QPF. In March, if you have that, right on the coastal plain is going to get warmer temps than Dec, Jan, and Feb more likely than not.
The majority of coastals in March come with marginal temps compared to the temps in met winter months and that just doesn't accumulate very good in the City especially with a stronger sun angle. Plus these coastals need to drop at minimum 2.0" of LE. Hard to get in March, on the coastal plain perfectly timed up with a strong arctic high.
The one thing that 1888 had that you don't get in March a lot these days is a nice strong, perfectly placed arctic high. That storm had that and brought it down to the coast. Temps were frigid on East Coast. Record lows and low-max's that day and the day after. That's basically what it takes to get a 20"+ storm in NYC in March.
Anywhere else in the Northeast, except for SE Mass/the Cape, has a much higher chance of achieving this in March, especially inland areas with higher elevation. Heck, it can happen in April in the NE, see April Fool's Day blizzard of 1997. Worcester had over 30" I think. Also, I think it was March 1958 or 1960 in Norfolk, Connecticut that they got something like 60" of snow for the month alone. It might have even been higher than that.
Point is, you need a VERY cold airmass to interact with a VERY wet system and NYC just doesn't have that great of a location for it.