When you create your currency (ERC20), you create a whole economy around it. The supply, inflation, price, etc. That gives you the flexibility to create your economy for your app. Plus, you may allocate some portion of the supply for the developer team, the community who supports and helps the app, etc. Having your currency is not necessary but gives you strong tools.
You can make transactions with ETH, accept payments, etc. You don't need a token (ERC20) to create an app. You can use ETH in your app.
It is all about your business model. How the app will survive?
- You may have ads to generate revenue
- You may have a commission on transfers with ETH, no ERC20 is required.
- You may have no ads and no commission. All services would be free if you have an ERC20 token to generate revenue by allocating some of the token supply for the app development.
The first option is the current business model of our world, which is terrible. Makes us the real product. The second option can be ideal depending on your app. The last option can be the best if the tokenomics is fair and well designed.
There are many things that an ERC20 token brings to an app. I can't list all of them. Last but not least, you can create a DAO to manage the app with the community.
You may use a discord server or a poll service to do that, but they can be manipulated. On the other hand, token-based governance creates capital-centric governance which is not a perfect solution. But you can create a non-transferable ERC20 token separately to handle governance more fairly.
I hope this answer helps a bit to understand the use case of ERC20 tokens.