That's correct, there is a write-performance hit for the reasons you say. All Raft systems will take the same hit, and SQLite is intrinsically single-writer -- nothing about rqlite changes that[2]. That said, there are approaches to increasing write-performance substantially. See [1] for much more information.
Write-performance is not the only thing to consider though (assuming one has sufficient performance in that dimension). Ease of deployment and operation are also important, and that's an area in which rqlite excels[3] (at least I think so, but I'm biased).
[1] https://rqlite.io/docs/guides/performance/
[2] https://rqlite.io/docs/faq/#rqlite-is-distributed-does-that-...
[3] https://rqlite.io/docs/faq/#why-would-i-use-this-versus-some...