The theoretical maximum number of satoshis in existence per person on earth is just short of 266,000. That's assuming all 21m coins are minted and that none are lost. I feel like this is already quite a small number if you want to represent a global currency, so can the system really afford to continuously burn away BTC at a relatively large rate?

You can always move the decimal point. It's all just software, it's all mutable if you can get enough people to agree.

(Not meaning to come off as a fanboy, I think bitcoin==beaniebabies. I just don't think the "bad coins" problem is actually a problem, even if you consider Gresham's Law. Physical currencies have been through similar things and survived).

Historically, BTC has not been willing to make changes like this. The community is culturally (and I would argue pathologically) opposed to even minor changes, which I think would be even more true when more divisibility would lead to potentially lowering the value of existing user's token by reducing scarcity. I'm not convinced such a change would be feasible given those constraints and if it's not the maximum divisibility of BTC is quite low assuming it becomes some kind of world currency - if I can only have ~250k 'units' of currency the smallest amount of 'money' I can spend becomes quite large.

It puts a hard cap on income inequality!

That’s not how it works. Income inequality is not just the “number” of coins but what it’s worth as opposed to something - with inequality it becomes everyday goods and services. The cost of goods can easily continue to worsen inequality. There’s only one real world soft limit - a revolution that resets the clock.