I also wonder if the author knows that you can modify the way track changes shows different types of changes (it sounds like she has everything in balloons, which could indeed be a nightmare with enough changes).
Something like GitHub for documents could potentially solve the collaboration issues, but I couldn't see myself replacing Word anytime soon. Word's formatting capabilities are unparalleled, track changes works well enough for my purposes (and better than anything else I've tried), and the cost and time spent implementing a new solution and training all of my coworkers would be too great.
This really is an aesthetic claim you're making, and it goes against what many in publishing feel, which is that substantial edits through track changes are clearly more taxing, less comfortable, less intuitive and uglier than paper.
You're also confusing collaboration problems with editorial workflow problems. The author is writing from a copy editor's standpoint, which involves producing clean, professional quality copy through a vertical, step-by-step editorial process.
Comparing apples to apples, the deletions and insertions in track are just as visually simple as on paper. The article's suggestion of more in-lining, if applied to comments on content from multiple editors, would be a nightmare. You wouldn't be able to fit some sentences on the screen; they'd be crowded out by all the interruptions.
The article also complains that small punctuation changes can become tedious. That's also true in either form, and the solution is probably organizational. You can reserve a punctuation (and S/V agreement, spacing, etc.) pass for right before publication, or just have a standing agreement that minor cleanup needn't go in track (just accept those yourself as you insert them).
I feel like the most significant failing of track isn't when comparing it to paper. If you're widely circulating a doc for comments, merging edits from a dozen commenters is its own special form of hell. That's true on paper, too, but not in editors that allow real time collaboration, like Google Docs. (That's admittedly a tradeoff, depends on how much you want a single individual acting as gatekeeper for all changes.)