Scenario: You are searching for something. You type "Foo Bar Baz" into the search box at the top of the page. The reults returned aren't what you want. You wonder whether a different language might have the results you want. The typical process from there is:
- Guess which wiki you want
- Go to that wiki
- Re-type the search into the search box
- Re-do any adjustments you made to the search (number of results per page? namespace?)
(Alternate approach, for advanced users: Hand-edit the URL to switch the language. But if you're not coming from an English project, then even the name of the search page has to be hand-edited.)
Suggestion: Why not provide 'interlanguage links'? They could be in the sidebar, just like interlanguage links. When you click them, they would run exactly the same search that you have on screen.