re: What's a "normal" amount of money for a late 20s person to have in savings?

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That's an interesting strategy - Wasn't aware there were no penalties on a Roth. Are there any other advantages to this other than tax savings, as opposed to doing this with a normal investment outside a 401k?

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The advantage is that your returns grow tax-free. Early on this doesn't matter much but later in life it certainly will provided you contribute consistently and heavily. And you probably won't be able to do that if you are diverting cash to an emergency fund that is taxable.

A psychological advantage is that most people will think twice before pulling from a retirement account too, which is perfectly fine. If you can put it off then it wasn't really an emergency to start with.

There aren't any disadvantages I know of.

Some people will say "you should never withdraw from a retirement account". My response is that if you are putting money into a taxable account first, then you aren't putting that money into retirement. Go ahead and do it now. An emergency fund is for emergencies, you shouldn't cripple the funds by putting them in a taxable account "just in case" when you don't have to.