I think you’d be right that the direct cost of running the crawler and index would not be the issue. But fighting SEO to keep your results decent is probably a cost that dwarfs the basic technical cost of running the crawler and index.
And you’d need a technical security team on top of things as link farms aren’t your only risk, I’m sure there are countless ways to manipulate the algorithm to put your site on top that Google probably have multiple teams working on fighting it full time.
Many of these things would likely not be a problem for a startup, though. No one is paying SEO firms big money to get into a search index no one has heard of and hardly anyone uses, so these costs probably grow exponentially over time as you become more well known.
Yes offering everything for free to prevent competition has been a surprisingly effective strategy for Google.