1. What's the "emergency" threshold to trigger a withdrawal? What I thought was critical in my 20's would now get a quick analysis and decision in a favor of a low or zero cost alternative. Pet medical treatment comes to mind - I spent $$$$ in my 20's on that at the cost of other savings.
2. Once the money leaves a Roth, you can't replace those dollars and their future compounding. I think the opportunity cost is too high to depend on Roth contributions for an emergency fund.
For number one, you could say the same thing about an emergency fund that isn't in a Roth. And everyone is going to have their priorities and values when it comes to what is critical whether they are drawing from an emergency fund, a Roth IRA, or building up credit card debt. I spent $$$$ on pet medical care in my thirties and then again in my forties, but I rarely ate out. My friends who were spending lots of money at restaurants and bars and expensive weekend getaways (while I didn't) thought I was crazy because of the money I spent on pet medical care. I still don't regret it.
In my mind, putting money in a Roth would have made the money seem more like a true emergency fund rather that just savings more generally, and I think that's probably true for others. In fact, now that I am 59.5 and old enough to withdraw from all my retirement accounts without penalty, I am having a hard time actually making myself do it because, in my mind, that money is for "later."
For number two, if you put money in a money market emergency fund instead of in a Roth that can be used as an emergency fund, then you still end up without the dollars compounding tax free. For a lot of people, especially young people, they are making the choice between the two. When I was young and paying off student loans, I wasn't putting money in retirement accounts. I didn't think I could afford to do that. Then, I was putting relatively small amounts in. It wasn't until later that I was maxing out.
I know someone whose parents started teaching her to save in retirement accounts from the time she started working as a teenager. She did end up eventually taking out some of the money from her Roth IRAs in order to buy a home in her twenties. But, so what? In the interim, she was building up money tax-free and she bought her house before houses got too expensive for her. In fact, now in her thirties, she not only has retirement accounts but also owns a second home that she rents out. She also runs her own business as a hair stylist, which she started at a pretty young age.