Politically, yeah. They're packaged together frequently.
But it isn't clear what avenue opponents of legacy admits could take. There isn't a law against the practice and Grutter expressly rejected the idea that legacy admits violate the 14th.
There are public schools that engage in legacy admissions, and that practice should end full stop. I admit that private schools are trickier to deal with, given that they have the right to control their own admissions process. Elite schools also don't have an impetus to change given the money that lies in admissions. I guess the NSF/NIH could make grants dependent on eliminating legacy admissions to create a monetary impetus to change, but there is a risk of hurting research if the Harvards don't play ball and it also seems ethically dubious to use research as a bludgeon to coerce admissions.
I think on principle, there's agreement here. The point that I poorly attempted to make is that it's a difficult task to impose a top-down, federal ban on legacy admissions from the federal administrative level. I'm not aware of any laws against the practice and the Constitution doesn't prohibit it. The only way to implement it would be to either shoehorn another law that wasn't intended to remedy legacy admissions in to do so (see, e.g., Obama Admin's Dear Colleague letter using Title 9 to convince colleges to combat sexual assault on campus) or to use monetary persuasion.
The idea of using grant money as a condition for eliminating the practice is a good idea and could be applied to public schools.
Either way, it's probably just a fun thought experiment, since a ban on legacy admits won't be happening any time soon.