Indeed, one of the concepts of a TOU rate, not necessarily driven by the Power Company, more from the Public Utilities Commission is that the should be revenue neutral. But their definition is more along the lines of "averaged out over thousands of users" So that means that some win and some lose. And in many cases, a standard rate is more like an insurance policy than a TOU is like raw cost.
First, many rates have seasonal changes, so make sure to look at summer vs winter usage.
When using a TOU rate, one of the basic concepts is can you move load from one time to another. If you are going to leave everything as it is, then you don't tend to take advantage of a TOU rate. So, when charging a car, that means that you will want to delay starting charge until the lower tiers go into effect. That's not that big of an issue, since the car supports it, but what happens if it takes longer to charge than the low rate period.
To really figure out what your cost is going to be, you need to look at what your usage is during the different hours, so that means you need something that can measure it. Knowing what your overall bill is, doesn't mean much.
But look at what your charging requirements are. If you are using 250 wh per mile, then that's going to be 1 kWhr for every 4 miles. Looking at
https://www.duke-energy.com/_/media/pdfs/for-your-home/rates/electric-nc/ncschedulers.pdf?la=en says that it will be about 8.7 cents per kWhr
If you look at charging 10,000 miles all at home, that's about $217 per year. Is it worth it to change for $18 per month? Just look at the gas bill that you decreased.
And caveat before people jump on. This is NOT California rates, this is Carolina rates, huge difference.