Database Files through Linked Servers
Powershell is the way. And it make it easier, just install dbatools on one of your admin servers and use get-dbadiskspace


  Get-DbaDiskSpace -ComputerName server1, server2, server3 -Unit GB


if you have list of servers then you can use 

$servers = get-content "D:\serverlist.txt"
foreach ($server in $servers) {
  Get-DbaDiskSpace -ComputerName $server -Unit GB
}


You can even dump the above info using invoke-sqlcmd2 into a central db for reporting .