Obviously, a lot of this devolves to simple personal choice. Here are my own, personal, rationalizations.
I've been using Powershell with SQL SQL since PSH v 1.0, and before SQL Server started officially integrating it. (When I started with PSH, I was administering SQL Server 2000 and 2005 servers.) So, I learned with SMO (or it's slightly older incarnation, the name of which escapes me at the moment) and .Net and I'm used to them. I'd generally lean towards SMO, since it makes some things a lot easier, like scripting out objects. My own code uses SMO some times and .Net some times. I think it's handier to use .Net to get simple result sets, for instance.
I think that Invoke-SQLCMD makes more sense if you have lots of existing TSQL scripts. If you are creating strings and executing them through -Query, that's going to be messy. If you have a good grasp of how Powershell works with .Net and SMO, using Invoke-SQLCMD occasionally, when you have a script file to run, is easy.
I've always found the PSDrive thing clunky and felt that they implemented it because they got caught up in the "everything can look like a file system" idea. I know that the *nix guys love \proc and such, but I feel that this implmentation feels sort of forced. I think that PSDrive is OK, maybe even good if you hate the UI, for exploring things but I've never written a script that uses it.
I have never seen anyone use the WMI provider. So, that would be my last choice.
So, I'd lead with SMO and fall back to .Net when it's handier to.
Access the backups files is controlled on the Windows end, not necessarily by SQL Server. SQL Server only requires that the account the SQL Server service is run as is given read/write access to the backup directory.
If you want another account to have access to the backup directory you will have to specifically add it to the ACL of that directory, or a group that might already have the permissions.
Best Answer
They don't require SQL Server full installation to view the execution plans. They just need the tools/client software, which they should realize this if they want to look at them.
They can use the following to view a plan file: