The Archive.org crawl is way too old to be of any use. And the Common Crawl corpus is only marginally bigger than what I crawl myself. There are currently just over a billion pages in my search-index and I can recrawl those about every 45 days. Crawling right now at about 650 URLs/s and 200mbit/s. Only about 60% of URLs crawled end up in the index. The rest are errors, timeouts, redirections, etc.
I have been thinking about adding an API. Rate-limiting is a must as you have correctly said. I'm already in a constant fight against SEOs who try to scrape the search-results and who apparently don't see anything wrong in making 10+ queries/second.
The API would definitly not be a free-for-all, but sort of like "send me an email and describe what you want to do with it, and if I like it I'll give you an API-key".Together with a primer on what not to do of course. :) If people do more than a certain amount of queries/month, then it would also have to be paid.