It seems to be such a simple invention. It could carved out of wood or made of brass and worn over the groin like a belt or an undergarment.
We’ve invented far more complex things but we didn’t invent a groin cup? Something seems off about that. Wouldn’t it help?
I’ve done kickboxing and that invention is definitely useful. So why wasn’t it invented earlier? Even for basic martial arts, was this invention just not thought of despite us inventing intricate armor and weapons, we couldn’t figure out a groin cup?
"Why wasn't X invented" is always a problematic question. You might equally ask "why didn't the Romans invent diapers?" -- they're useful too, but in their circumstances, wound cloth (swaddling) served them better. When it comes to clothing, bear in mind that the Roman had only what they could make out of natural materials-- contemporary athletic supporters and cups all use synthetic materials with tremendous elasticity, which the Romans didn't have.
The Romans had a kind of underwear, the subligaculum; its described being worn by gladiators and slaves, and seems to have had some negative association with effeminacy. Can't post images here, but you'll find very clear illustrations in the Villa Borghese "Gladiator Mosaic" from the 4th century wearing subligacula.
Soldiers did wind cloth and leather bands around themselves-- we find it described for limbs (referred to as fascia), not for the groin, but they may well have done. If you think about how athletes today "tape up" -- it might be something like that, without actually being a specific garment.
More generally, because clothes rarely survive we have a much less good idea of the fabric bits of clothing than we do of leather and armor. A pair of Roman leather bikini style underwear was found in an old well in London in 1953-- I think the only complete example, which raises the question "of what garments that once existed might we have zero examples".
Soldiers are practical people and routinely improvise ways to stay warm and protect themselves from injury-- many of these aren't part of the official kit. Just how a Roman soldier on campaign might have improvised on his equipment, we don't know. Roman armor was largely designed to protect from blows from above to the head, neck and chest, presumably the shield protected regions below that. Roman soldiers were expected to march a long way -- 20 miles a day- and you really don't want to do that with anything that is rigid and uncomfortable interfering with the movement of your legs as the miles mount.
Sources
The Retiarius Tunicatus of Suetonius, Juvenal, and Petronius
