They can easily last that. You gave to remember two things. They are used in qualifying, the first stint they're carrying a massive amount of fuel. Latter in the race they last longer.
You're saying something completely different, LASTING 15 laps while the tyres are being nursed isn't remotely same as tyres that can last for the same or even a couple less laps at full car pace.
You can go around at say, 1:42 a lap, for 20 laps, but the car is capable of 1:38, however if you do 1:38 laps you won't even get 10 laps out of them before they become useless. It's not that you can go 1;38 for for 5 laps then they just slow down to 1:42's anyway, you'd do 5 laps at 1:38, 5 at 1:42, and another 5 at 1:48 while risking going off the track at every corner, and going in for new tyres would ruin your race anyway.
I think kimi is the first person all season to go out on a soft tyre and gain on hard tyre guys, but he gained on the hard tyre also, he just had genuine pace. Both Mclarens went out on softs in the second stint last week, everyone else(just about) was on hards, and they were exactly no faster at all. If you save a set of softs, and use them in the race, you gain no speed because while over 1 second faster a lap the tyres at that speed, go off in only a few laps, so you end up doing the exact same pace as the hard tyre, making it worthless.
Everyone up and down the grid is going the pace their tyres allow, not the pace their car nor their driving skill allows, and that means we don't see the car pace, nor the drivers pace, but that set of tyres particular pace, that isn't racing, that is comparing sets of rubber, almost as interesting as paint drying.
I think part of the reason Hamilton didn't get ahead of Alonso at the end was, tyres and saving them, but the other part was very likely his team saying Alonso is going to get a ridiculously obvious penalty, and Rossberg too, so you're actually in a good position so just save the tyres and make sure you last to the end of the race, as everyone went in a couple laps early.
But that should tell you something, everyone went in a couple laps early because when the first guy goes in, the undercut can gain you several seconds, and the extra two laps doesn't matter because 20 laps later one guy has two lap older tyres....... and they are both slow as hell at that point. Everyone went in early because the tyres were starting to go, and almost everyone had just spent a stint saving tyres rather than gaining positions, then they all went in early, and all had to save tyres again rather than gain positions.
We've got both, tyres ruling everyones race pace, not the car, not the ability and to cap it off one proper lock of your tyres, one single corners mistake in 20 laps and hundreds of corners and you can kill any chance of catching the guy in front. Again, its not racing, its akin to watching football and not seeing who is the best team on the day, who plays the best football, its who has the best boots on.