Why is it important for individuals to be able to run their own nodes? I understand that the more people that can run their own node supports decentralization, but if miners are sufficiently decentralized what is the threat of users not being able to run their own nodes?
Every time you check your wallet, your wallet is displaying information that it fetched from a bitcoin node (usually with other software running on top of it, like ElectrumX). If you absolutely trust the server behind your wallet, then as an end-user, it's not necessary to run your node. However, you might still want to run it, because you care about bitcoin and want to help new users/companies download the blockchain, make the network more resistant to DDoS attacks or, if you live in an authoritarian nation like North Korea, you might want to make it harder for the government to censor bitcoin.

Running a node is especially important if you run a bitcoin-related company. In this situation, you shouldn't be relying on an external service as you don't know if it will be down, hacked or have bad intentions. 

Also, if you receive a large payment in bitcoin, you want to make sure you received it. You can check seven different bitcoin explorers but, depending on your level of paranoia, you might want to check your own node and verify that it has at least two to six confirmations.

Check out Andreas's video about this.