Unless something has changed, CVWs are not free! The tour given to parents may be free but the cost to attend (travel, hotel for parents if they come) is on the candidate. CVWs are primarily for the candidate. USNA now offers activities for parents -- these are designed to provide info for parents who may not have any idea was a SA is about. In the "old days," parents never came to CVWs. Parents do NOT need to attend if they can't afford to or if they already are very familiar with SAs in general and / or USNA in particular.
Also, NASS is no more "competitive" than CVWs. NASS is primarily designed for candidates who are from schools or geographic areas where USNA has historically been underrepresented. There are standards, but those standards are not the same as for a USNA appointment. So, for example, if you're marginally qualified and from North Dakota, your chances of getting NASS are a lot better than a more highly qualified candidate from northern VA. The fact you are accepted to NASS does not mean you will meet the standards for an appointment (though many do).
The use of CVWs has been greatly expanded. Years ago, CVWs were only offered to candidates who had appointments or were likely to be offered appointments. That's no longer true. Now, CVWs are used to provide exposure to USNA to candidates who were not selected for NASS. Thus, it's rare to be offered both NASS and CVW (though some candidates are offered both). There typically are more CVW slots than there are students who attend.
NASS has a cost component (other than those who are financially unable to pay) as well as cost of transportation. For CVWs, the only cost is transportation. Both are great programs. People debate which is "better." They really are just different. If you're interested in USNA and are offered either program, I highly suggest participating if you're at all able to do so.