I do not see any harm in applying. I would not expect you to be accepted. Harvard and Stanford in particular seem unlikely.
One issue is that I do not see any compelling academic reason for you to transfer. You are already attending a very good university. My understanding is that top ranked universities are skeptical of students who are chasing prestige, and instead are more receptive to transfer students who have a good academic reason to make the transfer.
However, completing your bachelor’s degree where you are, and then applying to graduate programs at any of these other universities, does seem entirely realistic. I got my master’s degree at Stanford, and the other students in the same program came from a huge range of other universities. A lot of the other students in the same program, probably a large majority, came from schools ranked about the same or lower compared to UVA.