I have not investigated any performance implications of doing this.

You should test if/how this affects performance because notes are also added by Odoo when specific conditions are met (record confirmed, edited) AND when Customers reply to emails.

Create the following Automated Action:

for record in records:
  if record.model:
    lead_to_update = env[record.model].search([('id','=',record.res_id)]).write({'write_date': datetime.datetime.now()})