Thanks! I'm so glad you're using RunKit and providing feedback!
So first, let me try to outline some of the things that happen when you hit "run".
To start RunKit parses your code finding all the requires, RunKit then load all your required packages (and of course their dependencies) at the appropriate versions. We also transform your code so all the latest ES features (which V8 doesn't fully support yet) are available (e.g. await). It's only after all that do we evaluate your code.
Now, I don't have the stats in front of me, but loading your dependencies and doing the code transform is probably taking longer than the evaluation itself. So even if didn't evaluate the code itself, it's unlikely you'd see any speed improvements from running your code in the browser itself (also the payload sent to the client would be much larger). As you mentioned, there are also certain UX features we're need to explore.
All that said, we're actively working on making things faster, with a focus on requires specifically!