I believe items in the sidebar should start with content that's most relevant to the page. So for a
/questions page it makes more sense to have tags that are relevant to the post appear first, and for the
/questions/tagged/* to first show info that's relevant to the selected tag.
If you access the Interesting Tags section of the sidebar often then I can see how the change in position can be slightly inconvenient. However, what works best for one person may not necessarily be suitable for the general audience.
Is it possible to customise the homepage in any way? I find it annoying that my 'favourite tags' move halfway down the page after I click on one.
It's won't be easy convincing the powers that be that interesting tags should always be on top. In the mean time, you can still make the changes locally using Userscripts. I personally user quite a few Userscripts to cater the site to my preferences.
Here's a basic one which pulls the Interesting Tags (if it exists) to the top of the sidebar: view (install).