I don't have the precise quote, but if memory serves, the original author of Emacs default keybindings is Guy Lewis Steele. You should be able to find a mention of this fact in the book Coders at Work by Peter Seibel. He described the rationale as being mnemonics-based. In your particular case, C-y stands for "yank", which was the word for what now is more commonly known as "paste" (or, sometimes, "cut").
I'm not sure, but would guess that M-w stands for "write", as in "write to memory".
Is there a convenient way to use vanilla keybindings with one hand? I'll be bold and say "no". They are designed to be used with both hands. You are not the first person to notice this, some long-term Emacs users had argued these keybindings aren't ideal. Steve Yegge and Xah Lee among those. This is, again, my opinion, but I see Emacs more as a DIY product than a prepackaged-put-into-microwave-oven kind of thing. This comes with benefits and downsides, one downside being that default keybindings might not be ideal for you. Luckily, there are already many ways to deal with this problem, Evil mode or Ergoemacs would be some of the examples that come to mind.