The idea behind using an engine is to not do most of what you describe.
Clobbering all this together in c++ is equal to making your own engine. While there might be situations where this is a good idea, it mostly is reinventing the wheel.
While you can carve wood with an axe, a chainsaw, a chisel and a sharpened spoon and even a blowtorch, what you propose is smithing a wood-carving tool.