I hope you won't think I'm rude, but LOL.
Seriously. you are raising a major issue. If you are working with a responsible company, you'll get the policy, pronto. If not, well no system is going to substitute for a plain old good work ethic.
UPDATE - Thought about this last night. If you are a lender, the simplest method for getting policies is to instruct title insurers to issue ALTA short form loan policies which are delivered with your closing package - no need to wait for recorded docs.
The problem we've seen with lenders who instruct us to issue the short form is that their post closing delivery folks don't seem to know or understand that method. We send the policies with the docs and then get follow up letters saying we never sent the policy. We even put the policy on the top with a big notice, highlighted, that says THIS IS YOUR TITLE POLICY. My guess is that those positions are manned by clerks who haven't a clue about title policies.