No, for a start some allocators don't even use sbrk (all mmap), and glibc's ptmalloc will use mmap for large allocations, ie you can allocate multiple megabytes with a single syscall with ptmalloc. Granted, if memory has been mmaped, you will pay a page fault because of the zero page optimization when you first write to it.
Furthermore, memory which is freed is often not returned to the os, either for fragmentation (you've used sbrk..) , or performance reasons (minimize syscalls), and put in a free list instead. The next call to malloc then will not require a syscall, if it can be satisfied with existing freed blocks.
Furthermore, memory which is freed is often not returned to the os, either for fragmentation (you've used sbrk..) , or performance reasons (minimize syscalls), and put in a free list instead. The next call to malloc then will not require a syscall, if it can be satisfied with existing freed blocks.