I'm pretty sure their purpose is to provide a source of wood before you have chopping tools and that is it. A less frustrating process than combing the floor for branches.

The wood game does get a lot more lenient later on though. Your charcoal kiln for example will become pretty obsolete once you discover that there is another infinitely renewable source of coal that does not require you to exchange wood.

And as you build up a portal network you will have access to a lot of different forests on your doorstep, even if that wasn't the original reason for why you placed down those portals to begin with. Of course each one will still demand increasingly longer walking distances the more you chop but a single forest should cover a solo player for a very long time, let alone multiple. Most people will naturally think to place a portal within convenient walking distance of each boss, and one player can certainly get by a whole playthrough on those surrounding forests alone.