ReSharper is amazing, and certainly not "for people who don't know how to write quality code on their own". It is also large, slow, complex, and its integration would require considerable effort from JetBrains, which is simply not going to happen at all. Ever.
It makes much more sense to request specific code refactoring features, preferably ones which would be straightforward to implement.

ReSharper is for people who don't know how to write quality code on their own.
Keep that bloatware out of the concise nature of LinqPad

In this blog article from JetBrains, they say "We’ve been working for several years in allowing ReSharper to work in different environments, independently of Visual Studio. An example of this is dotPeek." There's hope. http://blog.jetbrains.com/dotnet/2016/01/13/project-rider-a-csharp-ide/

As previously mentioned I doubt integration with Resharper will ever happen, but I don't see any reason we can't have a shortcut key mapping that is the equivalent to resharper. For that reason I've opened a separate suggestion here: https://linqpad.uservoice.com/forums/18302-linqpad-feature-suggestions/suggestions/11051385-resharper-keyboard-shortcuts please vote for it! :)

I agree this is unlikely to happen but I'd settle for some shortcut remapping (in Linqpad 5) to resharper's.

I don't belive that this is really possible. however, it is probably possible to use Roslyn for refactorings.

This would be amazing. I am sure that if plugin support was available then they could build it for LINQPad.

I have no idea how something like this could happen, but if it could, oh man...

even just extract variable would we super awesome :)

That would be cool, but I don't think there is the slightest chance it will ever happen...

Resharper suggestions/refactorings in LINQPad would be super awesome