I think that the ø7 symbol comes from a "classical" theory background, where the chords are analyzed using Roman numerals and the symbols are placed underneath the bass note of the chord. Originally developed from Baroque era (1600-1750) Basso Continuo, where a keyboard player and a bass instrument had just one piece of music to share, only the bass line was written out. Using the numbers and symbols under the bass note, the keyboard players would improvise right hand chords above the bass note in a stylistically appropriate way. Many times the harmony moves very quickly in this type of music, maybe a chord change every quarter or even every eighth note. When doing analysis in theory classes, there is often not much room to indicate the all chords in a measure. In G major, for example, the chord built on the 7th note of the scale would be indicated in classical theory as viiø7. If the 3rd of the chord was in the bas, it would be viiø65 (the 6 and 5 are actually written vertically, like a fraction.) This is still a big symbol, but F#m7b5/A is a long chord symbol that would mean the same thing. The slashes in classical harmony are used for secondary dominants, so they don't use them for bass note indications. I believe these symbols are used in analysis because of the function of certain chords in each key, for example, the V-I relationship. In jazz, the harmony often moves away from the original key signature, and the Roman numerals don't make as much sense in many tunes. And although the harmony sometimes does move quickly, a lot standards have 1 or 2 chord changes in each bar at most. Many players, of course, use substitutions and make more chords than are indicated on the chart, but the purpose of jazz chord symbols is to make them as readable as possible. I do think the m7b5 is a better symbol to use on a jazz/pop chart, written above the melody. Easier to read, IMHO, and better suited to the way that jazz harmony moves, with all the ii-V-I going on in many different keys in the same song, like All The Things You Are is a good example. I am an orchestra director in a public school (27 years) with a masters degree and I teach HS music theory as well. I also play bass in a jazz/pop combo on the side. I try to teach my students both methods of identifying chords, and I probably talk more jazz/pop than my college theory professors would approve of, but I think it is all important stuff to know. Also - I am always wanting to learn more, so please, if I have indicated anything above that you think is wrong or needs improvement, reply with your suggestions. My goal is to find the best way to teach kids about music, so I welcome any help from anywhere I can get it. Thanks!