It's a super good question. I would say two things here.
First, defining the ideal aesthetics is a really hard problem. When you start listing the various properties of curves (basically chapter 2 of my thesis), you find that there are relentless tradeoffs. Case in point: Cem Yuksel's C2 spline (cited elsethread) lists off a bunch of desirable properties, including local support, but then fails to be closed under subdivision. Turns out you can't have both. For the application it was designed for (taking a sequence of points from a hair simulation and defining geometry that can be rendered, preserving the continuity of the specular highlights), it's great, but I wouldn't want to design a font in it.
Another set of tradeoffs: the conclusion of my thesis is that the Euler spiral is the ideal interpolating spline for making smooth curves. So why isn't it more widely used? Two problems: first, you don't always want optimum smoothness, sometimes you want curves with high tension. Second, when you "push" the curve too far, the math doesn't converge to a unique solution, and the curve jumps around, which is really not a great user experience.
[It turns out that these two issues are related: I believe, but haven't yet firmly established, that by increasing the tension when deviation goes up, you can get a unique solution that's also continuous with respect to the input parameters. My prototype is promising but the solver is not 100% robust when pushed hard. It's a difficult problem.]
The second half of this is that Béziers occupy a really sweet spot in this tradeoff space: they're not as smooth as Euler spirals for making interpolating splines, but they're not that far off either. And they can represent high tension, inflection points, and it's easy to draw approximate superellipses, which is an extremely important family of shapes for font design and other tasks. The fact that the math is simple means you can do all the other computational geometry that's needed.
I am on that quest to define a better curve family, but it's pretty far from the top of my priority list right now, so I expect progress to be slow. It's more of a life goal than something I'm actively working on now. The reason this popping up now is that I used a few days during my vacation to revisit it.
First, defining the ideal aesthetics is a really hard problem. When you start listing the various properties of curves (basically chapter 2 of my thesis), you find that there are relentless tradeoffs. Case in point: Cem Yuksel's C2 spline (cited elsethread) lists off a bunch of desirable properties, including local support, but then fails to be closed under subdivision. Turns out you can't have both. For the application it was designed for (taking a sequence of points from a hair simulation and defining geometry that can be rendered, preserving the continuity of the specular highlights), it's great, but I wouldn't want to design a font in it.
Another set of tradeoffs: the conclusion of my thesis is that the Euler spiral is the ideal interpolating spline for making smooth curves. So why isn't it more widely used? Two problems: first, you don't always want optimum smoothness, sometimes you want curves with high tension. Second, when you "push" the curve too far, the math doesn't converge to a unique solution, and the curve jumps around, which is really not a great user experience.
[It turns out that these two issues are related: I believe, but haven't yet firmly established, that by increasing the tension when deviation goes up, you can get a unique solution that's also continuous with respect to the input parameters. My prototype is promising but the solver is not 100% robust when pushed hard. It's a difficult problem.]
The second half of this is that Béziers occupy a really sweet spot in this tradeoff space: they're not as smooth as Euler spirals for making interpolating splines, but they're not that far off either. And they can represent high tension, inflection points, and it's easy to draw approximate superellipses, which is an extremely important family of shapes for font design and other tasks. The fact that the math is simple means you can do all the other computational geometry that's needed.
I am on that quest to define a better curve family, but it's pretty far from the top of my priority list right now, so I expect progress to be slow. It's more of a life goal than something I'm actively working on now. The reason this popping up now is that I used a few days during my vacation to revisit it.