Vlad I don't know if I'm speaking for everyone but a usage cap of like 30 searches per hour (not 1 search per 2 minutes, as I very likely would do more searchws rhan 1 in a short timespan, while not going over 30/hour) through the API would be perfectly fine. And otherwise if I'd need more, then usage based billing.
Even 50/day would be fine for me, as I do on average 50 searches per day currently.
And I'd definitely would vote for unlocking the API only to paying customers. Otherwise the free tier would be abused even more...