As I know for playing Axie's you need to make an investment first... it's not a free-to-play game! Or I am wrong? When I wanted to try it I talked with some people about it, maybe they gave me wrong info about the game and I didn't bother much to check it out by myself, so I just decided to not try it!
You're right that it's requiring an investment for you to own an Axie, you have to purchase three of them and every Axie is sold or can be bought individually.
There's a rumor that there will be a free to play feature of it but you won't be able to earn anything. It's just a feature to make you experience how to play it.