Yes DOGE would be much better as an independent agency created by Congress with all the controls that comes with it. It’s inherently a bit toothless as an executive advisory council without further increasing executive power which is dangerous.
But I don't think employment is the primary waste issue. Federal employment has grown relatively slowly compared to local and state administration.
https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Go...
Which is why my point was about doing macro spending analysis. Most of the waste is in gov cost-plus contracts/procurement (feds outsource everything which is why employment hasn't grown much), how agencies operate (large duplication, old systems, etc), and more generally the unwieldy 1000 page congressional budgets no one reads.