D&D to me has always and will always be miniatures-based. It's a roleplaying addon to a wargame, for crying out loud. Miniatures attract interest. You can tell at a glance what's going on, which side is winning, what combatants are in trouble. Seeing 20 or 30 zombies set out on the table breaks people out into a cold sweat much better than mere words.
The grid helps eliminate DM favoritism (whether conscious or unconscious) toward those players who are able to more eloquently lobby for favorable rulings. It does away with the need for constant adjudication of the players' actions. Players can help each other out with reminders of positioning and tactics rather than having to channel every action through the DM.
Yes, I can make do without, but I find that any time saved on not mapping everything out is consumed by people asking for clarification or reminders on the current situation when their turn comes up. Maybe they could pay closer attention, but players are human. They go for snacks, use the restroom, answer the phone/door, and chat about life.
I actually dont disagree with any of this. You reasons are sound and they have been the basis of why I have used grids for the past decade.
Im just at a point in my gaming where I look back and ask myself, given I have played both ways, which I preferred. The speed and "imagery" of TOTM vs the accuracy and tactical coolness of the map.
I just find myself moving away from maps. Its preference. I wouldnt for a second argue that one way is better than the other and I wouldnt dictate that anyone is wrong for having a preference. I know what I like, and Im glad you know what you like.
We know how to support maps. I just hope that they do give some thought to this find a way to support TOTM.