On the other hand, this is the first time we've ever used our cards this way, after about 10 years of being on this path, and so from that perspective, it does feel like a relatively isolated incident. Although...who knows what the future might bring.
The way I am thinking about it, if we were to leave the $10k invested rather than sitting in a high interest savings acct. and then use our cards to cover unforeseen major expenses like what just happened, then it would actually not be the worst strategy. Even though it sucks in a moment like this to actually go through the process of selling shares.
There are people who use CCs as an EF, as you suggest. But two caveats:
1. You need it to be an intentional strategy, where you immediately execute the stock sale without debating your options. Here, you've been on the MMM path for 10 years, and you don't have either $10K immediately available for an emergency or a clear pre-existing plan to get those funds from some other source (as demonstrated by the fact that you felt the need to ask the question in the first place). That concerns me. You do want to have a plan so you don't have to think about it mid-crisis, which is when you're most likely to make the wrong choice. (Not to mention who wants to waste brain cells on $$ when you're in an actual life crisis?)
2. The "CC as EF" strategy can work out well long-term, because as you note, market returns tend to be significantly higher than what you'd make in a HYSA. But there are two downsides:
(a) Capital gains taxes will mean you have to cash in extra investments just to pay the tax. That reduces your overall return from keeping the money in the market. Sure, you can withdraw your Roth contributions, but that forfeits decades of tax-free growth and will cost you
way more in the long-term.
(b) When your plan is to sell shares, you risk selling into a down market, which means it could end up costing you more than if you'd just kept the $ in a HYSA. And I worry that, generally speaking, there is likely to be a correlation between major emergencies and down markets -- the economic forces that send the market down (like, say, a significant drop in the employment rate) can often be the same forces that create emergencies (like, say, losing a job). Most people have some degree of EF in HYSA to at least mitigate that risk.
If you're comfortable relying on shares instead of HYSA, that's perfectly fine; certainly, the long-term market numbers suggest that you may well come out ahead. Just go into it with full awareness of the potential downsides, and make sure you're comfortable with those risks. (Now is a good time to do that, since you're just coming out of a major hit, so you won't be as subject to it-won't-happen-to-me-itis).