I had the same thought, with the caveat that I'd be less specific than "barbell training". Adjustable dumbbells take up less space in a home gym, and with few exceptions and caveats, you can do all the same movements and progress up to advanced levels. I do currently use a barbell for deadlifts, but for squats I use Titan mini farmer handles with a Slant Stack (higher weight limit than 24" standard dumbbell handles but no need to make room for a whole squat rack), and for everything else I use dumbbells. (Well also a weight belt for certain things, but not any of the main lifts.)
Anyway, I haven't tried the app since I'm not really the target audience, but if it doesn't already, I do think that allowing users to put in a list of all their available equipment for the AI to factor in when recommending workouts would be great. Maybe even let it recommend equipment that aligns with the user's fitness goals and space/budget constraints (possibly as an opt-in feature), and slap on an Amazon referral code. A single 1RM deadlift or a couple bench press reps every now and then would do someone who would otherwise be sedentary much more good than grinding out a bunch of pushups or jumping jacks or whatever.
Of course, integrating potentially dangerous equipment and movements also makes proper form and safety guidance that much more critical, so it isn't something that I'd want to rush without proper testing. It'd be cool if it could watch you on video and give AI-generated real-time feedback, or at least provide recommended resources to find a personal trainer if you need one.