It’s kind of naive to assume that your CAC will grow linearly and your revenue exponentially if you set a higher price. Maybe if you’re lucky to find a market that doesn’t care about how much you charge them and get equally attracted to your product at any price rate.
More realistically price increases will increase you CAC because customers will take a longer thought to decide if they want to pay for that.
Maybe $5 a month doesn’t build a real business but you will be launching too late if you’re developing features that justify a $29 a month price.
It’s easier to launch at $5 and raise your prices as you build features. If you happen to have loyal early customers who never churned as you build those features, you can grandfather them into legacy plans and develop transition programs for them.
If you’re also expanding for their own use cases they will be happy to be moved to newer more expensive plans. They will most likely do it if you have been paying attention to their needs. And if they churn anyway, you’re getting 100% accurate data on the elasticity of your prices and the overall perceived value of your service.
Having a $29 a month service with customers doesn’t mean that your service provides a $29 value. It just means that you have a market where people are willing to consider a $29 value proposition until your value is proven to be less or when your customers find some other vendor with better price-value alignment. That’s when they churn.