Basically, as far as I can tell, you’re advocating pulling the “politics” out of “policy”, but that’s really damn difficult, perhaps impossible. Just stating it as a goal is not useful, without some kind of concrete proposal.
The people in charge are always going to advance their own interests, and there’s no way anyone has figured out to put a completely impartial and dispassionate authority in charge of a government.
The way the US does things (ideally; in theory) is to build a system of checks and balances in the government, and try to spread the power widely enough in the population (e.g. via elections of local representatives who meet together to make policy) that any particular group is unable to exert their will without some measure of consensus and cooperation from everyone else.
The problem in practice is that some groups have gained so much power and wealth, compared to everyone else, that they can game and coopt many or most of these institutions; meanwhile, other groups have so little power or visibility that they are effectively unrepresented.
I guarantee you, if you build an institution designed to be “empathy free” — for instance, some board of highly trained unelected technocrats — to make decisions, their process will be analyzed and gamed to the extent possible by the super-rich.
So, from whence comes individual rights? The usual argument is, "imagine if that were you!"--that's empathy. More seriously, we guarantee individual rights for others because that means we have them for ourselves.
This leads to my second point: I think the reason empathy even is a thing is that we are inherently selfish, and for anything to be really done for the "greater good" individuals need to either have a stake in that greater good or they need to trick their selfish selves into thinking they are actually in that situation too, which, again is empathy.
Empathy works for the most part. It sounds like the author is trying to fix something that isn't broken. I'd say the current problems in Washington are in fact a lack of both listening to data _and_ a lack of empathy. I think more empathy would be beneficial, not detrimental.
That's a viewpoint problem in itself. Liberties and individual rights should never be added because they are a 'net benefit'. I see the converse as being true, liberties and individual rights should only be removed if they are a significant detriment to society. In your example of gay marriage there is no data that it is harmful, therefore no reason to prohibit such actions.
Of course proving something is harmful is not a carte blanche to prohibit most actions. For example our 'war on drugs' motivated as doing good against the evils of drugs as turned into a rather harmful system in itself. Other systems that treat drug users rather than punishing them have much better outcomes.
Theoretically, I think a good first step would be to stop evaluating policies deontologically and start looking at results. There are so many laws in the books with good intentions but terrible outcomes, and they're all justified based on empathy and related emotional responses.
My argument is that we are predisposed, perhaps inevitably, to have more empathy with people like ourselves, and so removing empathy (rather than trying to fix it) may in some cases be the best way to get a fair result.