Yes, I've had the same experience. I contacted Rover to ask about this an their response was that Rover Now is the only service that they offer in NYC now for safety reasons.
When I joined Rover, all the information suggested that I would still be able to book walks directly through my profile where the service fee would be 20%, but this has been removed and now all walks in go through Rover Now and attract 40%.
I also have clients that would like to rebook their walks with me, but are now unable to because all walks get distributed to any walker in the area.
I'm certainly more selective of the walks I accept due to this and I find it a little demotivating if the client isn't even able to request me as a walker.
Below is an edit to my original answer based on new comments below. It is the response I received from the support team regarding legacy walking services and rebooking clients via Rover Now:
"In New York city, the dog walking option is Rover Now. Our traditional dog walking service may be available in select zip codes that are outside of Manhattan and Brooklyn, which would explain why you may be seeing "dog walking" as a service listed on some other sitter's profiles. Additionally, there are legacy users who can still book our traditional dog walking service with past walkers before the switch.
In regards to rebooking, the nature of the Rover Now service is so that an owner can have walks provided by any available and certified walker in the zip codes that offers the service. So rebooking in a sense can defeat that purpose, but we have heard feedback that a rebooking option would be favorable in instances where it's needed. I want to apologize for the information that is listed on the link you provided (https://www.rover.com/new-york-city--ny--dog-walking/ (https://www.rover.com/new-york-city--...)) There is misinformation on there, and I want to be completely transparent with you on that.
So to clarify, rebooking with a "favorite" walker is not an option between walker and owner on their own, this should mention the feature to "prefer" a walker. A preferred walker on an owner's account will be the first to be notified of an available walk before other walkers in the area."