The idea of the singularity presumes that running the AGI is either free or trivially cheap compared to what it can do, so we are fine expending compute to let the AGI improve itself. That may eventually be true, but it's unlikely to be true for the first generation of AGI.

The first AGI will be a research project that's completely uneconomical to run for actual tasks because humans will just be orders of magnitude cheaper. Over time humans will improve it and make it cheaper, until we reach some tipping point where letting the AGI improve itself is more cost effective than paying humans to do it