We all might benefit from distinguishing between "Likert" scales and "Likert-like" scales, or "Likert-appearing" scales. They really are not quite the same. Here's a brief background that I hope will help.
The specific procedures for constructing scales were developed before the 1960s so they are not "new" or "modern" topics to teach in college nowadays. However, the psychometric procedures of scale development always included quite a number of specific steps which, collectively, ensured that the final scales were truly interval scales at the least. (Some practitioners argued that they might even produce ratio measurement scales.)
I suggest you find a couple old references on scale construction and development if you really want to learn why any particular scale is interval instead of ordinal or nominal. I think Likert developed his scale around 1950, and Thurstone (equally-appearing intervals) developed his in the 1930s or thereabouts. Guttman developed his scalogram analysis procedures around the same general time period.
None of the final "short-cut" scaling products (e.g., Likert-like or Thurstone-like) by themselves can convey the logic or validity that a full set of scaling procedures build into those scales. By the end of the 1960s, however, most scale construction procedures were discontinued. By then, sufficient research had demonstrated that "Likert-like" shortcuts could produce results equivalent to the full scale development process.
In the late 1960s or early 1970s, the Journal of Applied Psychology devoted a full issue to this very topic. Findings showed a very strong consensus among psychologists and psychometricians that the considerable time and expense of scale construction could be safely eliminated when scales were written by people with sufficient psychometric education and training.
From time to time, the final condition of "sufficient psychometric" background has perhaps been taken a little too much for granted. Without a firm psychometric foundation, some simple-but-vital qualities that help to ensure scale validity can easily be missed during development. Just like anything else that can become complex, people who lack a sufficient background might very well produce invalid scales through a simple lack of knowledge.
People who use scale products as part of their professional careers should certainly have at least a moderate level of psychometrics in their educational preparation. If a college fails to recognize that connection then that college is producing graduates were don't understand an important part of their professional practice (an opinion).