Why does every app need full access to everything on my phone?

Many permissions are not necessary for the application itself however the permissions you mentioned are usually required by any app that requests them

It wasn't always like this, old Android devices didn't require any permissions to write to the SD Card and that was considered a security risk, nowadays you need to accept and acknowledged all permissions..

Sometimes an application needs to create files on the SD Card that aren't it's own files like download managers and file sorting applications, this requires a higher level of access to manage the files location or create new folders etc...

Obviously you should be careful when installing applications that ask for every permission possible, Like a game of tic tac toe that requires Bluetooth, NFC and internet would be strange and probably be able to hack your PayWave card from about 60cm away :0 true story