While the main reason to use base-10 is tradition as you've said, I think that in this particular case, the tradition argument carries a lot more weight than it normally would.
If you were designing everything from scratch, it *may* make sense to use base-16 from the start, rather than base-10. But we can't ignore the fact that base-10 is deeply ingrained, because this imposes a series of problems we would have to deal with in order to switch. In this sense, I think it would be a very, very, very long time (probably at a minimum several generations' worth of time) before any possible advantages of base-16 would make up for the costs (financial or otherwise) of the transition process.
Disadvantages of switching from base-10 to base-16:
- Most people have to learn a new number system (most people probably don't even know what base-16 is, let alone how to use it)
- Confusion regarding values represented by numbers in works prior to transition
- Ambiguity regarding values represented by numbers in works during transition (if you have the number 52, did the author mean that in base-10 or base-16? Most likely, not everyone will switch right away)
- SI system prefixes become harder to work with unless they are changed, in which case the world has to redo the transition to SI.
- Thought the fact that the US culturally refuses to use SI is confusing enough? Wait until any country decides they just don't feel like transitioning to base-16. Now, in order to understand any numerical values containing only the digits 0-9, we must know if it was produced in a country that used base-10 or base-16 at the time of production. At least with units, they have to be labelled, so there's no ambiguity regarding whether a paper intends a length to be interpreted in feet or meters.
- To eliminate any confusion, we'd have to start clarifying bases by some way, either by inventing new symbols for 0-9 in the base-16 system, or by giving a base label of some sort to every number. This will be much less convenient than the current system where we are almost always safe to assume a value is in base-10 if no base is specified.
- New number words would need to be created, at least in English, for numbers such as 2A (how would you even pronounce that? twenty-A?). New ones would also be needed in order to eliminate the ambiguity discussed earlier.
I'd say that in a realistic best case scenario, this change would create a situation where instead of just worrying about whether 1,234 is between 1000 and 2000 or 1 and 2, now we have to worry about whether 1,234 is 1,234 or 4,660.