What are some reasons one would want to apply the nominal value of a good or service in an economical analysis?

Technically, even the least bit of inflation will distort the real value of any measure. However, in most stable economies, we worry about inflation on a year-to-year basis.

If you are analyzing something about an economy within a specific year or even a more narrow time period, then the nominal values are just easier! I'm sure you realize that computing real values from nominal values is a complication. If I were thinking about the U.S. economy just for this month or the past 90 days, for example, I don't think I'd bother converting any nominal measures to real measures.

If I do any serious analysis involving comparisons from one year to another, I would use real values, even though inflation in the U.S. has been rather low in recent decades and in the past year or two. If I were analyzing anything in an economy like Venezuela, for example, I would not even compare month-to-month changes without converting to real values instead of nominal.