It's possible, but unlikely, that multiple emergencies will hit at the same time that completely drain a fully funded emergency fund.

This is like the joke about how you should always bring a bomb onto a plane if you're worried about a terrorist attack, because what's the chance of there being two bombs on the same plane? Just because you've already had one emergency doesn't mean you're less likely to have a second one. If you think that having 10k in cash is a good idea at time t=0 and lifetime cumulative emergency count = 0, then it's also a good idea to have 10k in cash at time t=1 and lifetime cumulative emergency count=1, and the only way to do that is to liquidate your investments instead of withdrawing cash.

That's what the cash is for.

You're arguing that you should do X with the money because that's what it was intended for. My point is that the original intention was flawed, because the design of an emergency fund as a cash-based first tranche of assets to be spent is misguided.