Yes.
For my specific plan, the daily rate (supply charge) has gone up from $1.13 to $1.80. That is a price regardless of any usage. This varies depending on what you select for your usage rates. So if you happen to get a lower per kWh rate, then your supply rate goes up.
Time of use also is manipulative. If you have a variable rate (time of use) then your peak time is much higher than your off peak which is higher still if you were on a fixed rate plan. If you select a plan that has 3 "free" hours then the peak time is rediculous priced.
So to sum up.. You have to have a very good understanding of how you use your power.
Home battery systems, and solar to some extent, are essentially 'pre-pay' schemes. A shift of where your money goes. At least for the next 7 to 10 years which is a rough payback period for solar/battery.
I would also like to mention, when Australia introduced the solar panel schemes, the retailers were paying 60c/kWh for infeed, now they are paying 1 to 2c. The high infeed allowed a home owner to offset their bills by infeeding while at work, sometimes even generate a credit just from solar. Certainly not these days. So what would be the next shift after they get everyone on home battery systems.
Lots of other stuff affects end-user prices though.