I agree that one needs to be realistic in targeting either of these professions and expecting to get in. At Princeton, about 3% of the campus goes into quant. And probably a larger (but still small) percentage goes into IB or similar roles.
Interestingly from the example of one of the firms that I have some anecdotal data on, for quant, it is mostly either CS with Math, or Math with CS. There are the occasional Physics or Mechanical Engg kids, but I am surprised by how small their numbers are. Perhaps there is a distinction to be made between Quant prop/ Quant funds on the one hand, and Big Bank Quant in roles such as structuring etc which are more open to engineers.