Upon Landing in the Americas the native populations did not have access to armor penetrating weapons like the Europeans did. Why didn't armor come back into fashion? I imagine being protected from native arrows weapons would be a pretty large benefit.
I only touched on it briefly when writing my thesis, but records from the Royal Armouries show* that the Tower of London was actually modifying and shipping its older armours to the colonies in the mid 1600s. Any breast plates that couldn't be "updated" (usually two of them roughly welded together :/ ) to withstand shot were sent to be reused in America for exactly the reason you state - they were still arrow proof.
How well it was all received at the other end is a different question however!
Alan Turton was doing some really interesting work on this, and gave an excellent lecture at the Wallace Collection which touched on the subject a few years ago ‘Building ‘Old Robin’s’ Army’, Fire and Steel…Arms and Armour of the English Civil Wars - but I don't know if he ever published anything on it, the Arms & Armour Society Journals would be the place to look if he did.
When Europeans arrived to settle/conquer America after Columbus, armour was still in fashion, and they certainly used it. The classic image of the Spanish conquistador includes breastplate and morion, and this isn't just a modern creation. From the Codex Azcatitlan, Cortez and his men shown well-armoured:
https://commons.wikimedia.org/wiki/File:Codex_azcatitlan222.jpg
The conquistadors also used native armour, of quilted cotton or kapok.
In what would become the USA, the early settlers brought armour with them. Their armour is covered in Harold L. Peterson, Arms and armor in colonial America, 1526-1783 (Stackpole, 1956; Dover, 2000). To quote Peterson,
The settlers who arrived at Jamestown in 1607 were well equipped with armor. There were both leather and steel targets for the targetiers, and there were jacks, helmets, and plate armor in ample quantity. In fact, when John Smith left the colony in 1609, he reported that there were more helmets and cuirasses than there were men.
Not all of the early settlers were that well equipped, but they did bring armour as space and finances allowed.
Peterson quotes from a Virginia law of 1611:
Hee shall not suffer in his Garrison any Souldier to enter into Guard, or to bee drawne out into the field without being armed according to the Marshals order, which is, that every shot shall either be furnished with a quilted coate of Canuas, a headpiece, and a sword, or else with a light Armor, and Bases quilted, with which hee shall be furnished: and every Targiteer with his Bases to the small of his legge, and his headpeece, sword and pistoll or Scuppet provided for that end.
which requires all soldiers to wear body armour (quilted canvas or metal) and a helmet.
Armour was already in use before European settlers arrived. In Mexico, quilted body armour was common. Further north, rawhide armour was common, often made with multiple layers, and sometimes including a layer of sand glued on to better resist penetration by arrows. Armour of wooden slats was also used. As well as body armour, shields were used. The native use of armour declined as guns spread more widely (sometimes following increased use of armour in regions where the horse arrived before gun, with the adoption of armoured cavalry), and it isn't surprising that the use of armour by settlers also declined.
For more on native use of armour, see David E. Jones, Native North American Armor, Shields, and Fortifications, University of Texas Press, 2010.
