I play piano, but I’ve never been actively involved in all of these "piano breeding systems", even though I want to be a part of them. So I put my eye on RCM. But I play at about an RCM 10/ ARCT level. Do I need to do any or all of the previous grades?
You can go straight in to whatever grade you think you can complete. Doing lower grades is a good experience for being aware of what actually happens in an exam situation, and also to show expectations of playing levels, etc.
Higher grade exams require a lot of work, and the playing level will need to be a lot more than just 'good' to attain a good score. There are also other considerations - aural tests, scales, arpeggios, sight reading come to mind, all or none of which necessarily will be easy for you as merely 'a player'. It also costs a fair bit of money to enter - even lower grades aren't cheap. So why would you gamble all that money - which is effectively what you may be doing.
Don't know at all about that exam board, but ABRSM for one requires grade V theory to be passed before taking grade VI and above practical. Not all exam boards have this inbuilt.
https://www.rcmusic.com/piano-syllabus-2015-edition-prerequisites-and-corequisites shows the prerequisites for the various RCM levels.
I'd suggest Level 8 would be a starting point if you believe you are playing at Level 10, but have no (or little) theory or history knowledge.