It appears that when U.S. Government agencies type "U.S.", they do not enter a space between the U. and the S. Is this used elsewhere on acronyms? Why or why not?
At one point in time it was common to see acronyms written with spaces (see for example "P. P.", which stands for "parish priest", in Ulysses, 1922). However, it's pretty standard nowadays to not include spaces between letters in an acronym. In fact, most style guides suggest using neither periods nor spaces between letters. Some style guides recommend using periods (and no spaces) only in certain acronyms. I have not found a modern style guide that recommends using spaces in acronyms.
The APA Blog recommends against spaces in "U.S.":
Generally, do not use periods in abbreviations. Some exceptions are that you should use periods in the abbreviations for United States and United Kingdom when these terms are used as adjectives (don’t abbreviate them if they are used as nouns). And if you have created an identity-concealing label for a participant, use a period after each letter.
Examples: U.S. Census Bureau, U.K. population, participant R.E.C.
This is explicitly said later on in the comments by the blog's author:
There should not be a space in the country abbreviation for U.S. The same goes for U.K.
Here are some more examples of style guides with similar recommendations:
Use no spaces after the periods in abbreviations.
The New York Times Manual of Style and Usage, 5th Edition
Abbreviations with periods should be typed without spaces between letters and periods
FranklinCovey Style Guide: For Business and Technical Communication
Note that names are often still written with spaces between the initials. For more info see Should there be a space between name initials?