Back in the day, Boston Dynamics made a slightly silly robot called "Big Dog" which received some DARPA funding. Also named the "Legged Squad Support System", it was intended to be able to walk alongside infantry across rough terrain and along narrow paths, carrying up to 150kg of gear which would obviously be good news for soldiers who might have to carry 20-40kg of equipment with them and even then compromises would have to be made.
The robot ultimately failed, not because it was a silly idea but because it was noisy as hell. By comparison, horses can move extremely quietly when required, so your military centaurs would immediately fit into this niche, fulfilling a requirement which would appear to be something that real world militaries actually care about.
They'd be less useful as actual soldiers though... they present a bigger target than a person (making them easier to shoot and harder to hide), they're not as manoeverable as a person (think about how a horse is going to do a 180 in a narrow space) and they can't easily make use of things like ropes, ladders or inconvenient staircases to access higher or lower areas. They can't operate vehicles without serious modification, they'd be a right pain to transport by air or by small boats.
Parachuting of mules is a thing that has happened in the past (there's an intrguing paper I can't find the full text of called Dropping of mules by parachute from Dakota aircraft) and as many as 1300 mules were flown into Burma, though alarming phrases like "the jerk of the parachute opening could burst their mesentery artery" suggests that there might not be many centaurs interested in
forming a pegasus unit joining the parachute regiment.
Finally, they'd be harder to feed and they'd need a whole additional set of medical skills and equipment in order to keep alive and well, presenting something of a logistical nightmare. There's not much in their favour outside of some pretty specialist roles.
I'd say their usefulness would have ended at some point before WW1... probably pre-Boer War, ~1900 (when British cavalry stopped using lances), but might have still been useful and relevant into the mid-to-late 1800s.