When you have thousands of subforums, the regular forum selector becomes absurdly long and thus no longer serves a useful purpose, and may also cause memory errors. Fix this by by switching on the level-based forum selector at Admin Panel -> Settings -> Switches.

With the level-based selector, submitters are prompted first to select a top level forum. When they do that, the subforums of that forum are shown for selection. When a subforum is selected, its subforums are shown. This continues until the bottom level is reached (though by not making a selection in the rightmost box the user can still submit to a higher level forum, unless of course you've specified to only allow submissions at the bottom level).

When clicking "submit topic" from within a forum, the page will have the forum structure down to the current forum already drawn out -- but ready to be changed if so desired.