Yes, its true that it makes it "worse" if multiple votes are cast and that was one of the considerations for avoiding it. But it would still take 50% of them doing so to get a 3/4ths majority on both sides.
In the general case of intentionally bad nodes, they can always cast different votes to different nodes and 50% bad nodes can cause an irreversible fork (that's the term I'm using for what you're calling an immutable one, figured it's best if we stick to just one term for it).
But avoiding two votes by good nodes prevents them from ever inadvertently behaving like a bad node, so practically speaking it is much better if they don't.
Intentionally bad I'm not concerned about here. I'm thinking of a "good" node that changes its votes but then the votes propagate differently. But if good nodes don't change their votes this can't happen.
I'm still not 100% sure about different situations with fork resolution. I'd feel better if there were a more detailed mathematical analysis, or clear reduction to a well-known consensus algorithm, but even without it may work "well enough".