I think it's important to highlight and understand that the symbols used to represent numbers are arbitrary; whether you use the symbol 'Z' or the symbol '3' doesn't imply the usage of a different numerical system, only that the representation in that numerical system is different. For example if the number system is using ZZZ to represent 333 (i.e. it's just swapping the representation of digits 0,..9 with equivalents) it is still ultimately using the Hindu-Arabic Numerical system. This is completely different to something like Roman Numerals, where the actual structure of the numerical system is completely different (e.g. 8 = VIII, there are completely different symbols used to represent e.g. 100, 1000, etc).
On the history of the Hindu-Arabic Numerical system and its spread, this is a
highly complex topic (to be very blunt anybody who claims it's down to 'imperialism' is too uneducated to claim they know what they're talking about). I would refer to St Andrews' University's overview of the History of the
Indian Numerical System and the
Arabic Numerical System for a full and referenced treatment, but broadly speaking the Hindu-Arabic Numerical system used today, which implies both a positional notation and a decimal base, has its origins in India (exactly when the positional system was developed is controversial), and around the 10th century AD began to be known in Europe and the Arab empire (although not widespread). It was adopted/modified by the Arab empire (as one of many competing numerical systems), and some cornerstone Arabic texts (notably the Latin translation of al-Khwarizmi's original text) featured and promoted the use of the Indian numerical system.
Around this time period (1200AD), Italian mathematician's (notably Fibonacci) became aware of this numerical system, and heavily promoted its usage raising awareness in Europe (albeit it was slow to spread and was initially mostly confined to Italy). The key reason for this is that the numerical system had major advantages over competing numerical systems, in particular, the notational system made arithmetic significantly easier and this provided significant advantages in trade, astrology, commerce, military, and construction (consider for example how easy it is to add 374 + 492, since you can compute it digit-by-digit, compared to performing the same addition using Roman Numerals and how you can represent significantly larger numbers without continuously expanding your digit set).
In the 1400s, in Morocco, al-Banna al-Marrakushi used a form of the numerals which is very clearly representative of the form of the digits used today, and would have been influential in Spain, and the development of the printing press (and other mathematical works around this time) combined with the superiority of the positional notational system massively accelerated the adoption of the system across Europe in the 1500s. The advantages of the numerical system encouraged adoption with other empires which came in contact (either in regards to trade or military applications) with empires (as there were many, not just European nations which adopted it relatively 'late') that were using this system.
While imperialism at a much later point impacted the usage of specific notation, the adoption of the numerical system largely came about because of the enormous advantages the Hindu-Arabic Numerical System brought compared to almost all contemporary systems.
Coming to the point of countries which primarily use a non-Hindu Arabic Numerical system today, I can't speak on that so will have to defer to somebody more knowledgeable on that aspect, but the historical context (and why so many cultures, countries, empires, etc. adopted it) I believe is important to understand.
EDIT:
Even in China and Japan, they use a mix. Generally, Chinese characters are used in places you might write out the numbers in English (one, two, three) while Arabic numerals are used for math, dates, passwords, and that sort of thing.
I always find it interesting how young European-style Arabic numerals are. Obviously they have routes in India, but they have only been popular in the West and in their more-or-less modern form for a few hundred years.
Arabic numerals have some inherent advantages for doing complicated math compared to Roman numerals or Chinese characters. Although, something being logical has never guaranteed its dominance. That I think is more down to geopolitical, cultural, and economic factors that their actual mathematical merits.
Saying 'some' inherent advantages is a significant downplaying of just how advantageous a positional system Is compared to what came before. While it's true to say "something being logical has never guaranteed its dominance", it's totally incorrect to apply that to the adoption of the Hindu-Arabic Numerical system. It was explicitly adopted both by the Arab Empire and European empires
because it was a logical improvement, and even the early introduction and adoption into Asian empires was explicitly driven by its logical superiority for arithmetical operations rather than geopolitical or cultural factors.This is a subject where the logical advantages were explicitly and demonstrably the driving force for the initial adoption (and that took hundreds of years)..
