I've never met a business stakeholder who gives two shits how engineering manages their work - all they care about is when am I going to get it and how much is it going to cost me - and how accurate and reliable are these answers?
As far as letting engineers manage themselves - if the scope of work is small enough and there's no dependence on other teams or vendors delivering needed components then sure, do whatever you want. It's often inappropriate to apply much rigor to such small projects. Skunk work projects can also be managed that way.
If your engineering department is being heavy-handed in how they apply project management to all their projects, then that's on them. But realize it is their job to ensure the work is getting done.