When you search for a house sitter, you should only see sitters who can actually housesit.
Unfortunately, house sitting is the service that is subject to the most interpretation by Rover sitters. I understand your frustration because I don't understand why anyone would offer house sitting and not stay at the home. I've even read comments here from sitters who don't even want to sleep at the home overnight but still offer that service. Makes no sense to me either.
You are going to find a wide range of interpretations from people who will move into your home and use it as a base of operations, while also doing some walks/drop-ins for clients to others who will only arrive at, say, 7 pm and leave the following morning. There are some who have other full or part time jobs or are students who may come back and forth.
Rover's FAQ states that each "night" of house sitting is good for 24 hours of care (just like boarding) and that the sitter stays in your home. Pretty clear to me. But each sitter on Rover is independent and can do whatever they wish. It therefore falls on you to ask potential sitters how the plan to fulfill the job and tell them your complete expectations.
Rover sitters decide what services they want to offer on the platform, some offer services they occasionally don't actually offer and I agree with you they should either remove them or manage their calendars better. But in their defense, if you are looking for a last-minute booking that can be very difficult to find regardless of the service requested.
Through rover’s algorithm that generates the search results, sitters have a vested interest in getting booked from a high percentage of contacts made. Which makes it even more dubious why someone would represent that they’re available for a service when they’re not.
Another tip to offer when you’re looking for a house sitter:
If your pet would do better without the possible addition possible of the sitter’s dog, when you search for a pet sitter use the filter criteria of Sitter does not have a dog. That will save time with those profiles that may not be a match. Reading through the profiles, you could probably have a good idea on whether or not the pet sitter would bring their own dog, but that filter saves time if you know your pets would not welcome another into the home.