I wasn't aware Pageant could work like this, and it is a good fill-in for this feature. Saves lots of time, thank you for the recommendation!

Did you consider using Pageant?

Or saving your common private key as default settings?

Or having a site template that you clone for each new site?

Somewhere along the way, loading the private key file got buried inside the "Advanced" options. I used an old version of WinSCP that was loaded on a machine recently, and remembered how convenient it was to have this selection right on the Login window rather than having to dig through the settings every time. My server targets change frequently, but use a common key, so saving the sessions isn't really an option. This would be great to have back on the login screen.