If you use a thread-local data structure, your allocator can pretend that it is running on a single-core, single-task system.
If you use a CPU-local data structure, you must handle the case where, mid-way through a call to your allocator, the CPU runs a second thread that makes another call to your allocator (and that, too, can get interrupted by another thread that allocates memory, etc.)
That makes thread-local easier to implement and likely faster (it doesn’t require any memory barriers in the fast path)
Also, good schedulers try to avoid moving threads between CPUs. The better they manage to do that, the lower the cost of having per thread data structures (there likely still is a price, as there most of the time are more threads than CPUs on a system)
https://google.github.io/tcmalloc/rseq.html
i don’t believe rseq based cpu local caches require memory barriers on the fast path.
Setting aside whether or not you can pull off a lock free approach here we can be certain of a couple things. There will be at least some overhead that must be paid somewhere even if that's on a separate management thread. And there will be a lot of additional complexity because that's just how concurrency always is.
Meanwhile the better the scheduler performs the more competitive the thread local approach becomes.