Formally right or wrong. All number systems "work" in the sense that they can represent numbers and be used for computation, but some are better than others.
Special good and bad properties. Properties are formal, but what makes them a feature or a problem are technological factors. For example, number systems with only 2 symbols are a good match for electronic circuits, but not for many types of mechanical calculator. Inventing different representations using 2 symbols is an interesting mathematical challenge driven from concrete applications; nobody thinks "inherent features of mathematics" are involved.
Fitness for a purpose. Nobody in their right mind thinks there is a "best" number system; it depends on what has to be computed and on a number of budgets and constraints; all applications require trading off representation size and/or electronic circuit size against computation speed (e.g. avoiding carry propagation in addition by storing 2 bits per digit) or initial and final conversion effort against computation effort (e.g. enduring BCD arithmetic because for few calculations it might cost less than converting to and from binary). Normal people don't have any particular "arbitrary and normative reasons" affecting these engineering choices; using bad technology (e.g. most arithmetic with Roman numerals) is usually the result of honest ignorance, not of epistemological biases.
Oh, we're getting somewhere. Yes! Also, consider these points with regards to such premises and elements' influences on the direction of practice, development and method i.e. working with 10 symbols might, surprisingly, isolate you from thinking about benefits which are not exclusive to working with 2 symbols but are more obvious and more familiarly practiced in 2-symbol representations. We've thought of some awesome things which have been developed for binary systems, e.g. two's-complement representation. These solutions were designed to emulate operation which doesn't necessarily depend on how many symbols there are. I've not encountered much furthering work regarding such potential. For example, matrices are a cool device which have been pioneered for many purposes that already had special methods but now can be elegantly generalized to a single form of representation; a matrix. Same applies for tensors. I hope mathematicians continue to innovate with representation in this way, but I've seen a lot of activity to the contrary in practical mathematics, particularly in the field of computer science. Don't forget to consider departing from a generalization to explore different sets of assumptions and vastly more appropriate representations etc.
I only disagree with your last statement, but we probably perceive epistemological bias slightly different to eachother. I'd be more comfortable to have a discussion about epistemological bias.
p.s. excuse my convoluted writing style. I'm slightly mad (as in, crazy) when I communicate. I can't form smooth sentences without taking the time to shave everything down. xD
using bad technology (e.g. most arithmetic with Roman numerals) is usually the result of honest ignorance
It's straight forward and easy but tedious and convoluted. Binary arithmetic is tedious but scalable and simple to implement. I honestly don't see what's so bad about Roman numerals. Of course we believe they're ineffective for most modern applications. I think they have merit and bear principles that have a lot of potential, but we deny them merely for the flaw of Roman numeral's character of complexity. Symbolic algebra is very complex and inelegant. Roman numerals use principles which could augment algebras to be much more conservative in their nature of expression and manipulation (i.e. simple and elegant to implement), and of course these principles stand appart from roman numerals themselves. I had this idea originally when evaluating two's-complement arithmetic and fixed-point arithmetic. The principles are quite congruent to the inherent procedural nature of Roman numerals. You probably think im batshit stupid now. Whatever.
I'm guessing you found some of their "variable names," offensive...
Fair guess.
