I can't think of a reason not to
Some of the tools don't support http, or don't need https, so the developers haven't added support for it in their tools. Other than that setback, I don't think there is anything to stop us from switching.
@tom29739 as far as I know, web access for all tools is managed through a proxy which supports https. As long as tools support normal http on a normal port, https works for free without any additional tool support.
I'm pretty sure the only exceptions would be cases where tools inspect the URL used to access them and freak out that there's an 's' in it.