No but yes.
No because you can't do it in the UI, you need to indulge in some coding.
But yes, because the coding isn't that hard (although it's well buried in the docs, the searches I tried didn't find it) - https://developer.atlassian.com/display/JIRADEV/How+to+create+a+custom+preset+filter
That covers adding your new filter, but removing "unresolved by priority" is a different matter - I think you will have to tweak core code in Jira to surpress it.
Personally, I'd leave the standard filter in there, but add your more relevant one(s). I am, of course, being lazy there, it's just less code change and less to think about during upgrade.
I won't ask why - I've been there. I find it rather amusing that there was loads of noise about it, I added the filters asked for and 3 months later no-one was using them because the standard ones were working fine. I quietly replaced their useless filters with a handful the noisy users had never mentioned and got lots of thank-you cake from the rest of the users. :-)
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