That's essentially a POC. Be prepared for many vendors -- including the company I work at -- to refuse, at least for most prospects.
The reason is some mix of 1. we have real onboarding / startup costs, and those costs are frontloaded; 2. like many saas companies, we don't make much money on the first year; 3. if a prospect can't commit, it's a sign that implementation is highly likely to fail. We require work and resources from the customer to make this succeed. To use examples you've given elsewhere, an ESP requires training, engineering to import workflows, creation of new mail rules, etc. An annual contract is a component of our executive buyer's leverage to hammer through the work to realize value from us.
What OP may be able to make happen is a POC with written success criteria. Be prepared for vendors to be hard asses about the success criteria however. We refuse these for small (enterprise small) contracts.
OP should consider that perhaps their vendor selection process sucks? Or maybe -- if they're a high enough contract value -- getting references from other customers?
Note also that people here decrying annual -- or multiyear -- contracts will be the first to scream if a vendor raises prices. Which is absolutely fair play if a customer doesn't want an annual or multi-year contract. A customer's right to alter a deal with 30 days notice is a vendor's right to do the same.