How can I allow access to form submissions only through email?

We are a web development company that would like to use contact forms on our account for our web clients. Can I create a form and allow our client to receive submissions to their email without full jotform access? Which account plan do we need for this?

You mean a copy of submissions when someone submits a form? If that's the case then you can simply use the notification for that: Setting-up-Email-Notifications

All plans including the FREE plan can create a notification. However, only paid users can create multiple notification templates or can add multiple recipients in the notification.

Guide: Send-Notifications-to-Multiple-Recipients

Also, the limits of the notification depends on the submission limit, please check our pricing page for more details: https://www.jotform.com/pricing/