I can rack up "life experience" up the wazoo (which I guess you do by not dying?),
No, you get life experiences by living through important emotional events.
Prime example: I'm assistant directing a show for a local theatre, and I'm working with two young actors (both 18) who have only just graduated from high school. As we go through the script, I find myself frequently asking them to draw comparisons between what their characters are going through and major events in their own lives. The problem I'm running into? Neither of them have had enough important emotional events yet to have a basis to draw upon for their performances.
For instance, in a scene where their characters, two young lovers, believe they are going to be separated forever, I asked both of them to think about what it's like to be dumped by a significant other. The problem, though, is that neither one of them have been dumped -- they've both only had one or two SOs, and they've both only been dumped once or twice in their lives, and not recently. Meaning, amongst other things, that what experiences they did have, they had at an age when they were far less emotionally developed than the characters they are now playing, giving them yet another hinderance. Nor has our male lead had the experience of feeling trapped in an unhealthy relationship, which is an emotional beat that plays an important role in his character but that he has no emotive or mnemonic connection to.
but I am pretty sure I am never going to become the next Derek Jacobi.
And as I said before, outliers are outliers. I'm talking about the vast majority of actors, not the ones that are so legendary they earn dual knighthoods.