Use an action rule. Set it up to trigger when criteria matches no tech assigned and status changed from open/pending/need info to resolved/closed. Action can be to force the ticket back open.
Or you can get around that entirely by making sure that all of your tech group levels are set to auto assign.
What other 'fields' are you referring to? Personally I consider everything above the request detail to be built-in and therefore can be configured in the settings to always populate. Everything south of the history section is a custom filed. The options for custom fields are hidden, visible, editable or required. So make them required.
