As someone who has watched a lot of subtitled Japanese animation, it seems odd to hear a word such as ninja (used in the plural) in the dialogue and see it transliterated as ninjas.
It somehow seems better to me to treat ninja just like antelope, bison, buffalo, caribou, deer, elk, fish, grouse, quail, reindeer, sheep, swine, etc., which are both singular and plural.
Would you also insist that Japanese speakers pluralize English words when used in the plural?
Once a word has been borrowed into a language, it adheres to the grammar for normal words in that language. We don't borrow Japanese grammar, just words, so there is no need to use a zero plural with borrowed Japanese words.
It is true there is a small set of animal nouns in English that have a zero plural, but they are not borrowed and are a special case.
This is borne out by the results in the Corpus of Contemporary American English, which has 68 incidences of "ninjas". Of the 496 incidences of "ninja", there are a handful of uses of "ninja" as a zero plural, as OP suggests, from the script for the 2003 film The Last Samurai, but the vast majority are singular (or attributive) usage. So it does appear that zero-plural "ninja" is used, albeit uncommonly so.
So yes, ninja meaning ninjas is a usage that gets some use, but regular pluralized ninjas is more common, and perfectly grammatical.
English has always had zero plurals as one of many types of irregular plural along with the regular plurals. For both borrowed and native words. So do related languages including German.
Neither transliteration nor Romance has a lot to do with it since we have nouns with both regular and irregular plural forms borrowed from Romance languages and other languages in the same alphabet and other alphabets.
In the case of ninja, it comes from Japanese and Japanese, like many languages, does not inflect for plural. Others are Chinese, Korean, Thai, Vietnamese, Indonesian, Malaysian, and all Polynesian languages including Hawaiian and Maori.
For Japanese it seems to relate to how mainstream a borrowed word has become in English. If it doesn't yet have wide currency or refers to something exotic it has a higher chance of retaining the Japanese (zero) plural. Here are some English words borrowed from Japanese in their plural form the way I say them, others may disagree:
We do this all the time with Latin and Greek loan-words in English. (The former is technically not a Romance language, but rather the progenitor of them.)
e.g. Octupus -> Octopodes (Greek), when we typically use "Octopuses"
e.g. Peninsula -> Peninsulae (Latin), when we typically use "Peninsulas"
There are many, many more examples, in particular of Latin origin.
Generally, because these words have been around so long in the language, we anglicise their plural forms, rather than keeping the originals, out of convenience (ignorance?). Some will always insist to use the original Latin/Greek plurals, of course. With more recent loan-words, it is more common to keep the plural form of the original language.
My view is that we should use the plural form of the source language when known/in common use, and anglicise the word by adding -s or -es otherwise. Each to their own, however.
I think the pattern is that English speakers pluralize with an "S" when in doubt, and some of the plurals that sound doubtful in English end in "A" or "I". As another example, I hear "schemas" on a daily basis, but never heard "schemata" except when I tried it myself a few times.
It's interesting that hippietrail refers to anime as an English word borrowed from Japanese, because anime is actually a secondhand loanword: Japanese borrowed the passé composé form of the French verb animer (spelled animé) to describe animation, for which there was no appropriate verb in Japanese. And so, English speakers are actually using a French verb to describe a Japanese noun.
And so, for me, the plural animes sounds perfectly natural in English.
Perhaps it depends on one's proximity to Japanese language and culture in everyday life. For E-J bilinguals, whether in Tokyo or LA, it is perfectly acceptable to avoid inflecting Japanese loanwords in English, especially in a code-switching context. However, the farther one travels from the Japanophonic (and Japanophilic) world, the more loanwords are moved from the "do not inflect" column to the "do inflect" column.
This is an organic, crowd-sourced process, not a hard-and-fast rule. Whereas Webster pluralizes kimono as kimonos, Wiktionary offers both inflected and uninflected plurals (kimono or kimonos). Webster has no right to take my kimono off, no matter how many of them I may be wearing! :-P
In response to the rhetorical counterexample of whether Japanese speakers should pluralize foreign loanwords, I have seen this occur in E-J code-switching contexts. Also, there is the annoying example of takosu (tacos), which has no singular form in Japanese, perhaps because tako is already the Japanese word for another popular food, octopus. Takosu-wo hitotsu kudasai! (One tacos, please!) Arrgh.
