I like an arrow rest on my self bow, and I think if you don't use one you should give it consideration. Not because I need something to hold my arrow, but because the arrow rest (or facsimile thereof) serves as a locator for the hand on the bow. My arrow rest is simply a piece of leather shoved down into the top of the handle wrap, so a bump is created, with a piece of soft leather on the inside of the sight window for the arrow to pass across. You can't be moving the hand up and down on the handle and expect consistency. The placement of the hand, up and down, on the handle is almost as critical as the left to right placement we just talked about.
Or, if you prefer not to have an arrow rest, anything which gives you a reference to bring your hand back to a consistent place on each shot. The point being that you need something that will remind you of how and where your hand goes on each and every shot from your bow. If your hand is in a different place, either up and down, or right and left on every shot, the arrow will go to a different place every shot. Promise.
This covers most of the things you are going to come up against when shooting your self bow. I suppose I've made it sound complex, but don't let that concern you. It only sounds complex. My desire is to give you enough information on how and why bows work that you will be able to solve any arrow flight problem you encounter. And that if one particular shot goes off the mark, you can say, "Oh, yeah, I... (your choice) on that shot", and correct it on the next one.
And, I know I've said this before, but it bears repeating: it's fine to reject everything that has to do with modern equipment and modern archery, but do not get caught in the idea of embracing inaccuracy and poor shooting as acceptable, just because you are shooting primitive equipment. Your primitive equipment can be shot as well as any other type of archery gear. You must know your tackle, how to shoot it, its limitations (if, indeed, any exist), and your limitations. When you go to the deer woods, responsibility goes with you, always.