I think equating ugly with hard-to-read is a common mistake. Many things are "ugly" but easy to read (e.g. in design circles, newbies often do far-too-small fonts with low contrast because it looks pretty, whereas accessibility guidelines tell you to do the opposite; in programming, readability of point-free style has more to do with the reader's ML-vs-Algol experience than how elegant FP may be, and educators often start w/ procedural style precisely because reading the flow of the program matches the students' expectations that things ought to be read top to bottom, rather than peeled through layers of abstractions)

Honestly, I find that rating the readability of the object versions vs the switch statement is bikeshedding. This is perfectly readable and doesn't involve going back and forth with my eyes to figure out the data flow or figure out if I have mismatched brackets or what have you:

    const getPosition = position => {
      switch (position) {
        case 'first':
        case 'second':
        case 'third':
          return position;
        default:
          return 'infinite';        
      }
    }

Another thing that is worth mentioning is that objects consume memory and allocating memory in JS for this is just wasting orders of magnitudes more cycles and sacrificing throughput for no good reason - other than to try to be clever and avoid an idiomatic and optimizable construct.