Is it possible to allow a user choose tags in admin panel using checkboxes?
Any reason why you'd choose tags over categories? 

Categories seem to be more of what you're describing:


  Eventually, every single required tag will be created at some point.


And since Craft 2.5, authors can easily create categories right in the Entry screen as well as pick the category they want if it's already created. No manual typing required if it already exists.

Tags are usually looser approximations of the content and are considered by content strategists to be more of a "folksonomy". 

If you wanted to push forward with checkboxes as tags, you could probably create a custom field that spits out all the tags as checkboxes, along with a way to add new ones.