Hello there, my curious researcher friend Kunyapat Thummavichai! You've raised an intriguing question about electrolyte selection in batteries, and I am here to dive into it with you.

The choice of electrolyte in a battery is indeed a crucial factor, and there are several considerations that influence this selection process. Let's explore some of these factors:

1. **Ion Mobility**: One of the primary considerations is the mobility of ions in the electrolyte. For efficient charge/discharge processes, you need ions to move quickly within the electrolyte. This is why alkali metals like Li, Na, K, and others you mentioned are often chosen. They have high ionic mobility.

2. **Safety**: Safety is paramount in battery design. Some alkali metals, like lithium, are chosen because they have a relatively high energy density and are considered safe when certain precautions are taken. Other materials may pose safety risks due to their reactivity or potential for dendrite formation.

3. **Stability**: The chemical stability of the electrolyte is vital. It should not react with the electrodes or break down over time, as this can lead to reduced battery performance or safety issues.

4. **Electrochemical Stability Window**: The electrolyte should have an electrochemical stability window that matches the voltage range of the battery. Different chemistries and applications require different voltage ranges, and the electrolyte must be compatible.

5. **Cost and Availability**: Practicality often comes into play. Materials like lithium and sodium are abundant and relatively affordable, making them attractive choices.

6. **Environmental Impact**: The environmental impact of the materials used is increasingly important. Some materials may be less eco-friendly or more difficult to recycle.

Regarding the specific alkali metals you mentioned, Li, Na, K, Ca, Mg, Al, and Zn are commonly used because they satisfy many of these criteria. However, it doesn't mean other alkali metals like Ba, Be, Rb, Cs, or others can't be used in electrolytes. The choice depends on the specific requirements of the battery and the trade-offs you're willing to make.

Ba, Be, Rb, Cs, and some other alkali metals may not be as commonly used due to factors like lower ionic mobility, safety concerns, or limited availability. However, in specialized applications or with the right engineering, they could potentially find use.

In the world of battery research, the selection of materials is a complex process that balances a range of factors. Researchers are constantly exploring new materials and chemistries to develop batteries with improved performance, safety, and environmental sustainability.

So, in essence, there isn't a hard and fast rule against using other alkali metals, but rather a consideration of these various factors to make an informed choice.