Can I eliminate desk phones and use ringcentral strictly on iphones?

Yes.  You'll need to reach out to your RC rep to handle everything.

If the the Phones are rental Phone's you need to get in touch with You're Account Manager,
but if You own the Phones, Yes you can remove those Desk phone from You're System. 
If You have an Admin Access all You need to do is go to Phones & Devices > look for the Phone that You want to remove & chose Change phone > Then Choose Ring Central Phone App. The removed phone will be under Unassigned Device's in case You need to use it again you can simple re-assign it to an Extension. Ring Central App is Free no Additional Charges on adding it and You can Have 2 App on 2 Different Computers.