Hello! I believe you are completely right: a separate tpl.php page for the homepage is one way to go about it, and is a good solution for many custom page needs. I myself haven't implemented that, but I've seen the method suggested in answer to many drupal.org forum questions. All it takes is a little willingness to learn to parse PHP; for tpl.php files, I find that isn't too hard. (But I haven't tried any really fancy tricks yet, either.)

I also agree thoroughly about having show/hide title (or other fields) as a per-node checkbox option; that would be wonderful! To have titles, teasers, author info, etc. all implemented consistently with a simple option for show/hide, as a part of Drupal core, would add great flexibility to page display.