*it's either a game (with judges and prizes) or it's Budo (of life and death matter)."
....or it can be both
Aikido is a way of aiki... It specializes in teaching aiki
Yes, takedowns etc are involved, but aikido is not focused or specialized on tactics so much.
Also most judo typically is not "even" on takedowns and ground and judo focuses on throws vice takedowns...although of course, YMMV.
Whatever ever you think Aiki is, can not exist, expressed, or developed without the physical.
What little I've seen of Aikido, the making contact aspects are limited and much of it presumed, but what to do with the contact seems to be focused on a yielding and blending the take-down with control. The Aiki inner-personal harmonizing aspects are wonderful with "harmless" people, in business and with acquaintances, but perhaps is not recommend with idealists that are committed to violence. Since I know I don't "know" Aiki, I have begun adding Aikido to my "Budo" practice.
Judo throws (and sweeps) are take-downs, dealing with the clinch. My favorate Judo quote is: "Conditioning is the greatest hold," by Karl Gotch.
BJJ strongly focuses on the competitive sport element of ground fighting and does an outstanding job of conditioning and of learning to deal with fear and pain that hones the confidence needed to think clearly to prevent or solve personal conflicts.
By the way, it's amazing how many educated (esp. the more erudite) people practicing martial arts hold on to many delusions about martial arts (and kindly show me when I do).