Score voting works perfectly fine with 2 choices. There's no basis to say otherwise.
Consider simple realistic hypothetical: what if 10% of the pro-Brexit voters are gung-ho and 90% are only slightly leaning toward it with a lot of hesitation; and 90% of the anti-Brexit voters are strongly opposed to the Brexit? With score voting, the pro-Brexit voters can still be majority but the decision will be voted down because the pro-Brexit voters weren't as sure. Even if the majority of voters decide to vote strategically, it would make a difference. I know I would never vote extreme one side or the other on something I myself actually feel conflicted about.
For clarity, instead of scoring 1-10 on "yes" as an option and 1-10 on "no" as an option, it makes more sense for yes/no votes to be on a standard strongly-disagree/disagree/somewhat-disagree/somewhat-agree etc. scale.
I'm not advocating for unanimous support as a mechanism. Tyranny of the minority is shitty, yes.
We absolutely know better ways that FPTP. Score voting is better, period. And just like FPTP can still put the post at higher than 50% (which is necessary for major systematic changes like this), score voting can put a requirement on what level of average score is needed to pass a measure.