There are ways of making customers able to create and browse issues without having an account. That's actually a very simple process. This way you don't have to buy an expensive license.
If you're interested I can link you to some material!
The most common workaround to this situation is creating a new permission scheme for your Service Desk project in which you allow the group "Anyone" to create issues and even Browse some if you want.
The only problem would be not being able to identify by internal user the one that created the issue in the first place, and for that you can easily create an obligatory custom field with the name of the reporter and other for his or her email.
You can also set JIRA to create issues via email and the reporter would get all the comments sent to his or her email.
I answered a similar question a couple of weeks ago, take a look:
If you're not familiar with setting permission schemes, here it goes:
Any further questions, just ask!
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
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