You can create an new issue type and change all closed tickets(that linked issue types that you no longer use) via bulk change. all older tickets can be displayed with new issue type. Do not add this new issue type to any schema.
after, you can apply @Jack Brickey steps, so you can hide isssue type that you no longer use from drop-down field.
yes that little slight-of-hand would certainly work. :-) I would suggest you create a reusable issue type, e.g. "Hidden".
I was going to suggest trying Properties to limit the issue types but I'm unsure if this would work for Issue Type and the initial status (Open) or not but certainly worth a try. I have used for custom field drop downs just fine. There is some Atlassian documentation as well as a few Community examples of how to set up properties to limit drop down choices. If you do attempt and cannot figure it out I will try to assist further later today/tonight.
...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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