Of course the libc allocator is slow, it's designed as a one-size-fits-all solution that's poorly tuned for most workloads and often doesn't get substantially updated for decades. By writing your own, you aren't avoiding an allocator, you're just avoiding the libc implementation of an allocator.
(In fact, most libcs let you just redefine the malloc(), free(), and realloc() functions to point to your own allocator instead of the default one, so you don't have to rewrite all the functions calling them. E.g., the mimalloc allocator [0] can be configured as a drop-in replacement for the libc allocator.)