Separate two questions that get conflated. Should evaluation be self-service? Almost always yes. Should there be a permanently free tier? That depends entirely on your economics.
Self-service evaluation is the thing that made the modern API economy scale. Before it, every integration required a sales conversation and a business-development process. After it, developers could help themselves — and a developer who can prove your API works before anyone has to justify a purchase is a developer who becomes an internal champion. Requiring a sales call to see whether your API returns useful data disqualifies you from most evaluations before they begin.
A permanent free tier is different. It has a real cost — infrastructure, abuse, and especially support, which is the expense people forget. Freemium developers consume support disproportionately. Be deliberate about what free buys and what it does not, and be honest that support is usually where free stops being free.
A workable middle: generous time-boxed trial credits, or a small permanent free allowance that is genuinely useful for a hobby project, plus a sandbox that costs you nothing. What matters is that a developer can get to a real response and a real answer about fit without a human in the loop.