Tell that to China.
The thing you are proposing is classic neoliberal mantra and does not help developing countries. Private corruption is no different from public corruption. What if a corporation comes and starts drilling after buying off some officials? Why do you focus on state corruption? That is not what is actually happening, it's mostly multinationals buying off local officials. Practical economic theory is to plan industrialization, utopian theory is about first setting up the perfect market and that things will then come automatically.
Are you saying China isn't corrupt or what?
As for the bolded, in a system with property rights, there is no need for any bribing of anyone. All you need is a buyer and a seller.
Multinationals bribing officials IS state corruption though, unless you are arguing that these officials are not part of the state.
The last bit doesn't even really mean anything, but China's 'planned' industrialization is not all it's cracked up to be:
https://www.youtube.com/watch?v=7enlEd_1XP4
Sure you can get outrageous rapid economic growth in the short term if the economy is run largely by state entities that don't really care about making a profit, but at some point the bill comes due, and it's going to be a steep one.