Intersection takeoffs
hadagutful-
It's not at all unususal (or unsafe) to do intersection takeoffs.
1. With a few exceptions, most carriers use "balanced field" V speeds. Meaning that as long as you have enough runway for your takeoff weight, the V1 will be the same, even if the runway is longer than required.
2. Also, with few exceptions, most carriers' SOPs require that once you've reached V1, the takeoff will be continued, regardless of the runway remaining.
So...if you need 6000' for takeoff and the runway is 12,000' long, if you choose to make an intersection takeoff with 10,000 remaining, no problem.
Of course, every takeoff is different, and the PIC evaluates each one. If there are factors to be considered such as slippery, icy, tailwinds, three engine ferrys, etc., an intersection departure would be ruled out.