Your question is, I think, better flipped around because Micronesia is by no means the only country that offers little to no travel restrictions:
To me the oddity is why countries don't default to giving a visa upon entry.
Strict border controls and modern visas as separate travel documents appeared around WW1. They did so chiefly because of security concerns, namely fears of espionage in an age where telecommunications had revolutionizing the speed at which a spy could send information and receive instructions. Another concern (particularly in the US) was controlling migration flows.
Since then, further restrictions on freedom of movement came for a laundry list of reasons - some utterly whimsical, some less - that depend on the countries involved. The various justifications given when travel visas get refused are colorful, but they give good hints as to why some countries require applying for a Visa rather than systematically issuing one to whoever shows up at the border. Key among them in my view:
- Controlling migration flows. It's not just towards developed countries, too; some developing countries reciprocate by returning the courtesy of the inconvenience.
- Controlling epidemics, for instance by requiring a proof of yellow fever vaccination when you're from a country where it's still common.
- Levying a travel tax in some form or another. It's usually one or more of a Visa or entrance or exit fee; at least one country (Bhutan) charges a fee per day.
- Militant or outright hostile attitudes. A Cuban Visa stamp, for instance, will earn you a hard time at the US border; likewise for an Israeli Visa stamp in a number of Arab countries.
- National security concerns - which is to say fear of terrorists.
The point in the above is to raise that issuing visas upon arrival is the natural continuation of what has been the natural state of affairs in most places for the better part of world history. And to shed light on reasons why that changed.
With this context in mind, your question. Micronesia, like a number of other countries, provides a visa to anyone that shows up at its border because, I'm guessing, they've few if any reasons not to:
- They've no particular enmities towards any country or group of people.
- There might be a vague case to limit the risk of spreading or reviving tropical diseases, but they already cover this by blocking entry if you come from an infested area without vaccination or certification.
- Actively restricting visas would involve a costly network of consulates and/or an administration at home.
- They collect a Departure tax already.