Those retailers, in my opinion, have it right; especially if so many of them agree that 1.6" for a base King is perfect for 2" squares. This is the standard size, so I'm not sure how you came to think that said-pieces look crowded.
Take note: on a 2.5" square board, the standard is a 2.0" base for King; on both sides of the 2.0"-base King is a leway of .25" before the next square. On a slightly smaller board, a 1.6" base King on a 2"-square board should have .2" (1/5 of an inch) on both sides of it (1.6" base King) before the next square. The scaled down version seems decent.
Just my .2.
What size pieces go best with a 2" squares board? It seems like a lot of retailers match up a king with a base size of about 1.6," but I find this a bit crowded. What are your thoughts, anyone?