I think pragmatic vs spiritual is a false dichotomy
Spirituality is about matters of the spirit: not training the body, nor informing the mind, nor improving mental agility, but strengthening the spirit.
So yeah, the discipline of showing up multiple times a week to do something difficult at physical and mental levels trains the spirit, but isn't special to Aikido.
Learning to face an attack without getting de-centered trains the spirit, but any combat art trains this.
Learning to face an attack without aggression or fear trains the spirit, but any budo focuses on this.
Learning to handle an attack without damage to the attacker trains the spirit, and is a particular focus of Aikido.
Learning to handle an attack without plan or strategy, but by being open only to the requirements of the moment, trains the spirit, and is the highest form of Aikido. But then, it's the highest form of budo in general. There may be many paths up the mountain, but when you get there, you're all pretty much in the same place.
So no, if I say Aikido is spiritual, it's not about Eastern mysteries or magic, and it is highly practical. It's about using Aikido as a tool to become who we want to be--in some dimensions, at least.