And now we are back at garbage collection - the two main options are reference counting GCs and collecting GCs. I know it for the .NET GC, they tried a reference counting GC and it performed worse than a collecting GC and not to forget the trouble with cycles when implementing a reference counting GC.
And reference counting also renders the point of determinism moot - now you never know if releasing a reference while trigger freeing a resource. You could of course delay offload it to a separate thread, but this makes you lose any guarantee about the time when the resource is actually freed, too.