Hey,
A way to do this it's to add a button on the search part with something like "search on each folder".
Like this we've the first search is on the current folder, and after that the user can choose to search on all folders with a lazy loading for messages during the search.
And this option can be disable on admin if it take too many ressources.

Bandwidth is not important. Most IMAP servers are very slow on search, even for a single folder. But I admit in some cases where folders contain not so many messages it can be useful. Still, it's the feature which is currently too complex to develop. All existing features (and the entire mail engine) assume the list is a single folder contents. The ability to have messages from different folders in the list is somewhat very different, entirely new concept. New paging mechanism, dealing with operations when messages from multiple folders are selected (e.g. it found messages from inbox and from trash, I selected them all and clicked Delete - what to do if some messages are already in Trash - i.e. messages in different folders can have different rules of how to process them), and many more design questions to resolve. In other words, this feature is dangerous - it can lead to UX decisions so bad which would make the product harder to use then if this feature never existed. We'll do it eventually but only after very deep thinking and rethinking of all the aspects.

Well, but if the webmailer itself runs on the mailserver or a webserver which is within the same host machine and connects via internal virtual lan via 10 Gbit/s this should be no issue or?

Main problem with this, in terms of our application, is that we're dealing with email messages on IMAP server directly, and IMAP supports searching within current folder only. In theory, it might be possible to run separate search for each folder and then merge the results, but we wouldn't expect any decent performance here.