Why goods prices are normalized in each period in growth models?
In fact, in growth models, people usually assume that there exists a one generic good for which the price is equal to one and not an infinite number of goods. Then, it is possible to set the price equal to one. 

You can look at Acemoglu's Introduction to Modern Economic Growth textbook. In this book, you can see in a decentralized economy (where there are different sectors, final good producer, intermediate good producer etc.) you can see that the price of the final good is normalized to one and there exists a price $p$ for the intermediate good. 

Therefore, to sum up, in simple canonical solow model with only one sector, there exists a one generic good and for more complicated growth models (endogenous growth models), where there are different sectors, there are different goods, then this implies different prices.

Hope that is a clear answer for you !