I've used bin log for almost decades and never experienced a big performance impact. This even holds for write heavy MySQL instances in ancient times where servers had spinning disks.
Nonetheless its not a WAL, and if you are not replicating it idk why you'd have it enabled, and if you are replicating you must.
Thinking back about it, I think the biggest issue was the size, not performance. For a write-intensive app, the bin long quickly got to tens of GBs and filled the entire disk, which was a problem when running the app on smaller VPSs.