With my experience though I found that trying to limit signups to prevent abuse caused so much friction for legitimate users that I actually decide to change my strategy to the following:
1. Allow essentially unrestricted access to the free account on a separate domain/hosting so that people don't feel the need to churn through accounts with bots etc. and the load can be separated out. Hence this page: https://www.exchangerate-api.com/docs/free My signup form actually automatically redirects some classes of disposable email, bot signup etc. to this page!
2. Make sure that anything particularly resource intensive or that's a good reason to sign up for my service is only accessible after payment. I would love to give out more functionality for free but unfortunately the people that take advantage mean it's just not economically possible.
So for me the main reason to get an email address is 1.) so that users can have a better experience - get usage notifications, updates about the API that might affect them, share the account with a colleague etc.
And 2.) so that business users can be satisfied. Pretty much anyone running a company that is relying on an API will want to have an account, see how the upgrade process would work if they needed it etc. even if they're only starting off with a free plan.
Basically hand out tons of short lived credentials right from a widget on the main landing page, together with each API response giving a link to a signup form that can convert the key into a fully fledged account.
Thanks for the suggestion!