User with admin permission on a space can't see Browse Space, Space Admin, Layout link.

EXPLANATION: PLEASE READ BEFORE COMMENTING.

In order for Confluence layouts to display the information they do, the templates must be given access to a wide range of internal Confluence data and functionality. This means, however, that a the templates themselves are actually more powerful (can see more information and perform more operations) than a space administrator.

It is feasable, given a well-written layout, that a space administrator could grant themselves the power to do anything a global administrator can do.

Because of this, layout editing has been limited to global administrators only. If you want to give someone the power to edit space-level layouts you may as well give them global administrative access, because effectively, that's what you would be doing anyway!

The only real solution to this problem is to redesign, from the ground up, how space look and feel customisation works, providing a limited, safe set of capabilities (and probably a custom templating language). This is something we're considering for future Confluence development, but obviously it's a significant task and not something we can just implement overnight.