What kind of near-immediate effect would a thorough, accurate proof of P=NP, with a provided solution, have on the practical world?
There's likely a great deal of great things that would come of it, but nobody would care.
The problem is that the foundation of (almost) all modern encryption is based on the assumption that P not equal NP. The encryption that protects your password as it goes over the internet, and as it's saved in databases. The encryption that protects credit card data as it goes over the internet... The encryption that protects the billions of daily financial transactions that tie our global economy into the giant organism it is.
Best case, P = NP means that stops. People go back to using cash and banks try to record these cash withdrawals on some disconnected medium since transactions to a central office are no longer trustworthy. This lasts for maybe a few months until better encryption is implemented globally. Best case.
Worst case, P = NP means that someone breaks the world. Currency is built on the concept of trust. You value a dollar, because you trust that your neighbor will give you a dollar's worth of goods or services for it. You value your computer saying you have 500 dollars in the bank, because you can swipe your card and get 500 dollars worth of goods and services...
What if you couldn't trust that? If P = NP, someone could impersonate various banks, government, people - and effectively randomize the amount of currency in every account. Delete the currency in every account. Sure, various banks have backups to account for it, but how long has their encryption been broken? Which transactions were good, and which were impersonated? It's impossible to know.
Once that trust is broken, chaos ensues. Any benefits from being able to deal with the Travelling Salesman Problem (for example) are ignored as people struggle to feed themselves.
Reality is likely somewhere in between, but hopefully this paints a big enough picture of how important a problem this is.