There are a few things going on at the same time that mean that electricity cost might actually go down.
The reasons for that are complex but have to do with how electricity pricing works. In many markets the price includes a lot of taxes, fixed cost for providers and infrastructure. Generation is only a minor cost. And on top of that the prices are set in a way that isn't really that flexible.
Infrastructure utilization is a very important here. Grid operators are very conservative with their infrastructure. They want to ensure there's enough to handle the worst case. That means there are a lot of assets that are nowhere near 100% utilized (e.g. cables and long distance transmission). It also means they are very inflexible serving new demand like data centers.
Adding batteries as energy buffers enables a lot better utilization of all these assets. That enables more revenue for the same infrastructure cost. Electricity prices can actually go down if you do that right. With renewables, there is very low marginal cost for generation. It's all infrastructure cost. Anything that improves infrastructure utilization enables more customers to have power that then share the infrastructure cost.
Data centers that are currently powered by things like on site gas turbines are not being very cost efficient. There's an obvious incentive for hyper scalers to invest in infrastructure that will lower their cost. They have access to many billions. They are spending on anything that will get them energy. They are desperate to spend. And they are completely bottle necked on grid operators that are being very conservative. Hence the expensive side hustle with gas turbines. There's a big opportunity here for massive investment in better grid infrastructure. That wouldn't necessarily be payed for by consumers. But they would still benefit from better infrastructure.
The key is unlocking these investments to happen.