I have filed several cases for damages and received most of the reimbursement from host guarantee with no problem at all. The key is that you need to follow the guideline PRECISELY. Here's the information website.
https://www.airbnb.com/help/article/361/how-do-i-request-reimbursement-under-the-host-guarantee
The procedure is that you need to use "send or request money" in the resolution center, and upload all evidence. There might be chances that a responsible guest would just pay for the damage, but most cases not. After 3 days, or if guest declined your request, you can go to resolution center and involve Airbnb.
Specially pay attention to this term: "Note that requests must be submitted either 14 days from the guest’s checkout, or before the next guest checks in, whichever is earlier." That means you need to start the request BEFORE the next guest checks in. Basically if you have guest checking in on the same day, then you only have a few hours to complete the request.