I've noticed that fairly often, my inputs don't do anything? Anything from holding right to start running immediately after the loading screen to jumping to increase speed on ropes has a small chance to completely be completely skipped over by the game, often leading to a dead run. I really hope we can get an explanation so that the game can be less luckbased

I don't remember experiencing this when I did runs. For those individual cases though, sometimes if you start holding right too early it won't work. Start holding it just before you get control. And for the ropes, you may have just let go of A too early, before you touched the rope. I'd recommend holding A from midair, this will make you jump off the rope on the first frame, though it's harder to control your jump height this way.