I could answer this question every easily. Of course they should. Although they may be able to afford to pay for their own studies, if they deserve a scholarship, why should anybody stop them? Why would we want to set a limit on the amount of money a student gets? If they get more, they will probably be able to put it to better use, seeing as they merited it.
In many countries, normal government aid is out of the reach of the wealthy, given that they are means tested. This means that one must prove that they cannot afford to pay for everything themselves. As a result, they are discouraged from trying any other sources. This might seem fair on the surface. Most scholarships are means tested, but others are based purely on talent. These are merit-based scholarships. Earning it depends on being good enough, of course, and not just being.
There is also the question of how many children there are in each family, The more the children, the more likely they are to qualify for aid as sometimes it is dependent on the number of children in the family. This is a very real concern. For many wealthy families, particularly in the West, they have more children than the less well-off. As a result, although they might earn more, it is split between more family members, who might each be left with relatively little.
The next point to consider is something much more concrete. This is the fact that a family’s financial situation could change, either for better or for worse. In some instances, it can be for worse. This means that applying for means-tested scholarships will pay off, because it will simply mean updating your family’s financial situation. Once the account is reviewed, then corresponding eligibility will be updated and acted upon.
Finally it will not being fully dependent on one’s parents. This is a a skill which is very important. While the Bank of Mum and Dad gives great rates and often does not need to be repaid, it should not be fully depended upon. The scholarship application process is also practive for other applications that the student will eventually make.
As we can see, there really are not any reasons for the wealthy not to apply for scholarships other than the fact that it could be seen as greed.