It has a sensor and only goes off for overheight vehicles. If you see it come up, you will hit the bridge if you continue straight, but it's worded too like a generic warning to all vehicles: which is the parse you have also apparently made.

Better wording would be "Overheight! Do not proceed under bridge!". If you have space: "you are overheight!" or "overheight vehicle detected!"

Add the number plate with an ANPR camera for bonus "this means you" (it also triggers a red light phase whenever it sees an over-height vehicle, so you will have time to read it). And yes, this is possible, I've seen supermarkets flash your number plate at you as you enter to warn you the parking times are being recorded.

I see what you mean, you're probably right that it would help, but honestly I just don't think the people hitting it are reading it in the first place. It doesn't light up until they're at the intersection, at which point they're either very focused on the light or the traffic, and definitely not looking way above even the yellow bar. Most people seem to be driving rentals, and in their case they're just not thinking about the size of their vehicle, and the rest have gone under a thousand bridges that look to the unfocused eye just as tall, so they're not worried about it at all. What they really need is probably just something that hangs at that height in front of it so you can hear it bang off of your car with minimal damage before you actually hit the bridge, and push the intersection further away from the bridge so there's more time to look at the signs.