The cost of inflation (at, say, 3%) is $30 for every $1k you have in your emergency account. That's $150 per year if your emergency fund is $5k, or $300 if it's $10k.

I'd be surprised if the combination of the effort it takes and the fees that are charged are less than that for your method.

That being said, it's sounds like you have a firm grasp on your system and it works for you. That's much more than can be said for a vast majority of people.