It might be dangerous to craft a statue of the Holy Spirit.
In the Old Testament, Israel, in a period of weakness, crafted a statue of a golden calf and started offering sacrifices to it. When Moses saw the calf, he become wrathful toward Israel and toward Aaron, who initiated the idolatry to begin with.
The golden calf was supposed to represent God, but God himself didn’t seem to happy about it, as shown when Moses, his faithful friend, ordered the execution of around 2,000 or 3,000 persons.
I imagine a similar scenario happening should statues of Doves, representing the Holy Spirit, be built and presented. Some Catholics might end up falling into idolatry, such as animal worship.