OTOH, it is a much cooler slogan than 'education paid by society at large :)
That is far from clear. There are crazy people on the left just like there are crazy people on the right, and I think some of them really don't understand how the world actually works, and that you really can somehow magically make education "free for everyone".
Even if it's not true, it provides ammunition for the opposition to say that it's true. One way or another, I think using misleading terminology is generally not a net win.
When leftists say that something like public healthcare would be literally free what they mean is that the net cost compared to the alternative is null or negative, not literally that nothing is being spent.
If you want to give me a link of someone who literally thinks that free college means that no one has to pay anything for the college itself or it's staff, I'm willing to take a look. Otherwise, it's just an argument that the net cost to society is negligible or negative, which is a valid use of the word too.
Of course, not many people have the concept of money at the government scale either. What does $75B to Ukraine really mean?