8 hours of marching, 8 hours of long rest, the remaining 8 hours are rest stops, meal breaks, regrouping.
You could definitely do 24-32 in that time. And your feet, legs, and back would ACHE from it.
As to the "You're wearing full armor!" argument. Full Armor isn't THAT heavy. Sure if you're wearing a full set of plate armor with associated padding, maille beneath, straps, and such you'd be looking at 30-50 pounds (Depending on style and your specific body structure). But unlike a Backpack, that weight is distributed across your form. Some of it is resting on your hips. Some of it is resting on your shoulders. Some of it is supported by straps squeezing across your torso, or arm, or thigh, breaking up the weight into more manageable pieces.
Because it was -designed- to move and fight in, which meant it couldn't be overbearing in any one aspect, or wear down your energy level too drastically since it'd leave you stranded in the middle of a battlefield if you collapsed from exhaustion.
Though, in all honesty, I would tell my player "You cannot travel overland in heavy armor without significantly losing speed unless you are mounted" And I have done so in the past.
And since heavy armor (and short legs) slow you down in combat, slap the "Slow" speed on anyone wearing heavy armor (or under 4ft in height) for overland travel. Make their "Fast" into unarmored (tall people) normal.
And heavily armored halflings move at a crawl. MUAHAHAHAHAAAA!
I mean... Break it down. The 24 hour a day march is 8 hours of walking. 24/8=3. Can you walk 3 miles in an hour and still have time to take a quick potty break, snag a cup of water, and get a few minutes of rest before doing it again? Then you can get 24 miles in 8 hours.
If you can manage an 18 minute mile you're capable of a 3 mile per hour speed with 6 minutes of faffing about and making no progress. If you can do one in 15 that gives you 15 minutes of faffing about. And if you walk a 12 minute mile, that's a whopping 24 minutes of just chilling with your friends on the trail.
24 miles in a day is very reasonable.