Because those fights are fought under different rules and with different styles because of the gloves. Many bare knuckle fights that'd last hours were because they lasted until either someone was dead or unconscious or quit, the notion of a ref stopping the fight once someone got a harsh cut didn't exist. Beyond that, because of the risk of punching e.g. the jaw without gloves (it'll break your hand fairly quickly) punches were directed more at the body, hence the boxing stance where the hands weren't close to the head as much to protect it as it wasn't necessarily the prime target in the bulk of the match.
Of course it'll last longer, doesn't mean it'd last longer under similar rules and fighting styles as boxing is today.
My point is that 15 rounds of the type of punch volume to the head simply wouldn't occur without gloves. It might still be a long fight, but you won't get anywhere near the same type of volume to the head. Hell back in the day there was grappling, kicks and arm locks back in the day. Similar perhaps to MMA, punching the face wasn't nearly as big a thing as it is in boxing today, and a big part of that is because of modern rules as well as boxing gloves.
And again as I mentioned earlier, it's not the broken hands that count. (they can cause permanent damage, yes). It's the permanent brain damage that is the biggest concern, and that risk has increased much more now that gloves make it possible to throw hundreds of punches to the jaw and not injure your hands.
If you're trying to argue that I said that gloves extend fights longer than they did under bare-knuckle rules, you're right, that's not true and that wasn't my point. What I meant to say is that they extend the fights in which fighters mostly punch to the face much longer than they normally could, and radically increase the volume of punches to the face (without reducing the impact to the brain, instead, increasing it, as the weight of the gloves increases the impact).
Although I think it's probably possible to contest the following quote, it's not far from the truth and illustrates the differences a bit:
> As the bare-knuckle campaigner Dr Alan J Ryan pointed out: "In 100 years of bare-knuckle fighting in the United States, which terminated around 1897 with a John L Sullivan heavyweight championship fight, there wasn't a single ring fatality." Today, there are three or four every year in the US, and around 15 per cent of professional fighters suffer some form of permanent brain damage during their career.