Our org is at least 10 years old. Consequently, lots of records have inactive users listed as the Organization Owner on Household Account records. As a nonprofit, we don't care who the record owner is. I would like to change ownership of these records (using Data Loader) to a generic user we use for automated processes. Any drawbacks to proceeding down this path?

Hi @Christopher Lagarde, I recommend that before you change anything to first do a full data backup of your org. Go to Setup > Data Export > full export and download the zip file.
Also, there is a Mass Transfer feature in Salesforce that you can use to mass transfer records. See documentation here: https://help.salesforce.com/articleView?id=admin_transfer.htm&type=5
This utility allows you to transfer accounts as well as the following records related to those accounts:
- Any notes that belong to the existing owner.
- All contacts that belong to the existing owner.
- All opportunities (including closed opportunities if you select the Transfer closed opportunities checkbox below) that belong to the existing owner.
- All open activities assigned to the existing owner. Note that completed activities will not be transferred.