I'm not an economist either, but my armchair take is that the value of a particular currency depends very much upon the perception that the entity who prints the currency will maintain the status quo (i.e. they won't unexpectedly go bankrupt tomorrow).

I believe what would happen with a single world currency is that it would generally be very unstable due to things like war, economic policy that proves disastrous for one or more of the members of that currency club, and as a result it would become untrusted.

For instance, recall the US housing crisis of 2008-2009. This caused massive economic damage, and resulted in the United States printing money at unprecedented levels. Imagine now that the world utilized a single currency and one single nation faces a similar crisis. Would the world be expected to accept that the entire currency should be devalued due to excessive money printing simply because a small member country couldn't keep their shit in order?

To frame this idea in a simpler fashion, imagine a single person named Scott who creates their own currency. That person hands out the currency when purchasing goods and services, and later on people can come back and spend that currency in order to purchase Scott's belongings. This works pretty well because Scott never hands out currency that he isn't able to back up with his belongings.

Now imagine that there is a group of ten people who print their own currency, and you can use that currency to purchase the belongings of any of those ten people, regardless of who gave you that currency. Let's imagine that Scott is by far the richest person in that group, and Carlos is the poorest. When Scott hands out massive amounts of money for legitimate goods and services, that money can now be spent amongst any of the ten members. Let's imagine that someone decides to spend that money to purchase the belongings of Carlos. It turns out that Carlos does not have enough belongings to sell compared to the amount of money possessed by this spender. Nonetheless, all of Carlos's goods are purchased in one fell swoop (before inflation even has a chance to show itself), and Carlos now has zero belongings.

Now imagine that instead of being a person, Carlos is a country. No one living in that country would be able to purchase goods anymore, because they were bought out. This would result in ridiculous inflation (meaning that the purchaser of those goods received a massive discount compared to the real value of the goods purchased in that place), and the country's economy would essentially be broken with no fix on the horizon as long as they continued to use that same currency.

I think it's important to remember that currency isn't just printed paper, but a promise that you can redeem that paper for goods and services. When an entity is no longer able to provide goods or services then the currency that entity uses loses value because it cannot be trusted to be redeemable in some places. If that currency happens to be the common currency used by the rest of the world... well, sucks to be the rest of the world I guess.

Keep in mind that when a country which uses their own local currency experiences economic problems, they can still purchase more reliable currency using their unreliable currency, and then purchase goods from that place reliably (even though that other country won't be able to do the same). Because the other country cannot reliably purchase goods from the economically compromised country, they will impose a very high exchange rate based on the risk that the exchanged currency will not be redeemable. This is the essential quality that local currencies possess, an exchange rate. Exchange rates are what keep global currencies sane, and based in reality.

TLDR: The value of a currency depends upon the ability for holders of that currency to redeem it for goods and services. The reason the dollar is strong is because goods and services from the United States can be reliably purchased using the dollar. If the United States magically ran out of goods to sell then the dollars they printed would be worthless. If the entire world used the same currency then it would be all but guaranteed that the currency would be unredeemable in some places, and as a consequence the value of the currency would drop.