Up until about a dozen years ago, I don't recall hearing anyone pronounce niche as "neesh." I have checked a few dictionaries and most only list "nitch," but some do include "neesh" as an alternative. At least I never hear "nee-SHAY."
Anyone else take notice of this?
That has been my experience. It's as if it sprang from nowhere, which is probably not the case, but that's how it looks from here, on a slightly different coast from yours.
I wouldn't expect to hear nee-SHAY unless it were spelled niché.
I have long believed NEESH to be proper when used in a medical or scientific sense, and the pronunciation given in Stedman's mediical dictionary backs that up. The ordinary "hole in the wall" sense is usually pronounced NITCH. It may be that people overhear discussion of an ecological NEESH and feeling undereducated, adopt that pronunciation as their own for other uses.
It's not unheard of for medical/scientific pronunciations to be different. An obstetrician will report that a baby's crowning is at 8 centimeters (SOHNtimeters) - meaning the diameter of the circle, but talk of "five centimeters (SENtimeters) per second", when talking of a linear measure.
When I studied biology in high school, a half century ago, we all said nitch. Of course, that's because Mr. Bach said it that way, but as torpeau and I have mentioned, it's only in the last decade or so that I've heard any other pronunciation in any context. Well, in English. French is a different matter.
Even though I've never heard nee-shay, I wouldn't be too surprised if I were to hear it. I often see cliche , negligee and resume in English spelled without any diacritical mark. OK, I don't see negligee nearly as often as I would like. But by analogy to cliche, niche might easily be mispronounced.
Think of lingerie. I mean think of the word lingerie.