If you ever played FFXI, Adoulin introduced Mog Garden. It's essentially what OP described more or less, and... it doesn't cost anything to have one, just need to do quest to unlock it.

And I agree though, XI's Mog Garden should be carried over to XIV. Kinda stupid that players need to sacrifice alot just trying to grow their farm which already involves delicate task compared with XI's gardening system.