Yes, there is a reason for that.
Best known in Missouri (because that's where they originated in 1952), the black letters in the white square indicate a
Supplemental Route, which are roads within the state which the MDOT was given to maintain in addition to the regular routes. The goal of the secondary highway system was to place state-maintained roads within 2 miles (3 km) of more than 95% of all farm houses, schools, churches, cemeteries and stores. The four types of roads designated as SUpplemental Routes are:
Farm to market roads
Roads to state parks
Former alignments of US or state highways
Short routes connecting state highways from other states to routes in Missouri
The
United Stated Manual on Uniform Traffic Control Devices (MUTCD) lays out in mind-numbing, excruciating detail every little thing about every little sign on every single road in the US. Well, technically, not every road. It lays out the standards designs for highways in the Interstate and US Highway system.
The familiar blue Interstate shield is the only trademarked shield in use in the US, and the familiar US Route shield was inspired by the Great Seal of the United States. The MUTCD provides default designs for state highways (the boring circular highway shield) and county highways (a blue pentagon with yellow text), but the states are free to use whatever design they like for state and county roads. Currently, only five states (Delaware, Iowa, Mississippi, New Jersey, and the great commonwealth of Kentucky) still use the breathtakingly boring circular shield for state routes. A few states still use the circular shield for town-maintained sections of state routes, but use a different shield for the other parts of the same highway. Maryland, for example, uses the default circular shield lor locally maintained sections of state-numbered highways, most often in
Baltimore, but otherwise uses a different design elsewhere for the same state route. Several states use the outline of their state as the shield (Ohio, Florida, Arkansas, Missouri, etc.), while some use other outlines, like the beehive of Utah, Pennsylvania's keystone state design, Kansas uses a sunflower, Washington uses a bust of George Washington. California uses an acorn-looking shield for its state routes. Actually, it's supposed to represent the spade carried by the Forty-Niners into the foothills and sold by the opportunistic merchants who made the real fortunes of the California Gold Rush. Now you know. It's a spade.
Some U.S. counties also have unique shield designs, though most use the MUTCD default.
So those letters inside the white squares are nothing more than lettered roads, instead of numbered roads. In most cases they are state maintained roads, even if they are a county road or a state road, but not in all cases.
There is an entire Web page dedicated to KY road sign goofs, from misspellings, to arrows pointing the wrong way, wrong road numbers, and wrong shields. Here's one that is still in place after at least 15 years, along KY 859 at Avon, just north of I-64 in Fayette County, where if you go straight you're on KY 57 and if you go left you're magically on US 57. US 57 has it's eastern point at I-35 about an hour south of San Antonio and heads west to Eagle Pass where it goes down into Mexico. Nowhere near Kentucky.
So, with all road signs, you get what you pay for. Except you really don't.