FYI, you don't have to write short replies; this isn't chat, and it isn't Discord.
The basic thing missing from your scenario is: how does your fuse know what voltage it's at? Voltage is a difference between points, and the voltage drop across a practical conductive fuse must be normally small so its power loss is small. All the bits of wire know is how much current is flowing through them; they could be at 0V to their surroundings, or a million! There's no way to tell what voltage is across the actual load, so it can't possibly control that voltage.
In fact, this concept can be used to "game the system", say to test equipment used at high power. Consider a monitoring system used on medium-voltage distribution lines: it might have 14kV AC on it normally, and sense currents over 100A. That's over 1.4MW of continuous power! (2.4MW even, since it would be three phase.) How do you test that without your own power station? We can apply the 14kV AC to the voltage-sensing terminals, and loop a different wire through the current sensor -- well insulated so it doesn't care about the 14kV nearby, and can be sourced from an ordinary transformer or whatever. Typically such a system would use a magnetic current sensor (current transformer (CT) or Hall-effect), so that a wired connection isn't required to sense current, just a loop around the wire being sensed. The voltage source then only needs to deliver ~mA, and the current loop ~mV, so the total power dissipated by the test equipment is small (~W?), but the EUT (equipment under test) reads up to full power. You've successfully fooled the system! The catch is, the current being measured is not, in fact, part of the full loop across the 14kV, it doesn't go out and return through the two points being measured across -- and the EUT can't know that, it just assumes you've wired it the right way. But in fact you've made a sneaky loop around it, so you don't need to dissipate anywhere near a megawatt to test it. Handy, eh?
Which also means, to make such a fuse, it needs to be wired correctly. If it's sensing voltage, but switching current, it must be a three-terminal device. There's no guarantee that the user wires it across the appropriate three connections, but you would document your device accordingly of course. But anyway, we need to somehow construct it to do that.
You could make such a thing by simply putting a heating coil around the thermal fuse bit: the more voltage is applied, the hotter it gets, until it melts and opens. This is a very slow-acting and crude method, but just to hand-wave a possibility.
There is also another interpretation to your question.
In the same way that a "current-sensitive fuse" operates (when current goes too high, current is forced low and voltage high), presumably a "voltage-sensitive fuse" operates exactly inversely: when voltage goes too high, voltage is forced low and current high. That is, instead of blowing open, it "blows" shut; an anti-fuse!
And, note that an anti-fuse would be a two-terminal device, applied in parallel to the load, exactly opposite of a fuse applied in series with it.
And indeed, such a component is useful for protecting current sources, where the open-circuit voltage could be dangerously high, and shunting it to ~0V significantly reduces the power output of the source, just as open-circuiting a voltage source (what are commonly in use) significantly reduces its power output.
The deeper truth here is: circuit theory, at least, is symmetrical around voltage and current, that is, we can swap them around, and exchange series and parallel connections, and get an equivalent system. We can use fuses in series with voltage sources, or antifuses in parallel with current sources. This is also where the Thevenin/Norton ideal source equivalence comes from.
(As it happens, there are physical reasons that prefer voltage sources, and we typically have to go out of our way quite a bit to make a good and proper current source as such, but circuit theory at least makes no such distinction, and we can draw circuits that work equally well with CCS or CVS.)
Tim