I don't think most of the world really cares about dollars.
Maybe not, but most of the world HATES decimals in prices. Decimals confuse people. Would you like to see a cup of coffee cost 2 milliBits or 0.002 bitcoins? It's much easier to understand whole numbers. Also, many people think 1000 $ /bitcoin unit is too expensive. I try to tell them they can buy fractions of a bitcoin, but they hate that idea. People don't like dealing with fractions. It's basic psychology.
This is the reason I'm in favor of using the unit 'bit', where one bit would be 100 satoshis. it would be so much more marketable. Getting a fraction of a BTC for a dollar isn't very appealing, but getting ~1000 bits would sound a lot better. Bit derives naturally from bitcoin, but is still different enough that it sounds like its own unit rather than just being a word for a thousand or a millionth of a BTC.
The following quote from another thread justifies it perfectly.
+1 for 1 million bits in a coin. I feel like that would be perfect when 1 btc is in the ballpark of $10k, therefore a bit is in the ballpark of a cent. Its still workable now but its also looking forward to the future. With a 10k valuation, prices for things won't need decimal points, they'd look like dollar prices do today except without the dot which I think is very intuitive. Bits is easy to say and intuitively derives from bitcoin.
Too many names for things is confusing, especially when they can be confused with each other like milli and microbits. Now we'll have bitcoins for large sums, bits for small sums, and satoshis for the technically inclined (laymen need not worry about this term).
Bits also work if bitcoin ever reaches a valuation of a million $ each, then bits are equivalent to dollars and prices can reintroduce two numbers after a decimal point like we use now.