I haven’t done it but I used to work in customer service and one of our workstreams was for dealing with complaints to the ceo or other higher ups. Generally this was something that you had to be seen as reasonably competent to be assigned to, it was only done by the in-house staff, not the outsourced team, and they got more time to deal with each complaint.
Obviously don’t go into it expecting to actually speak to the ceo or anyone who works directly with them, but it probably is worth doing if you’re having trouble getting what you need through the general customer service route, as you’ll probably get through to someone who is incentivised to actually help you rather than just reply to your email in the least possible time.