Yes. But most of the cost of the ticket will be operating expenses for the train and associated service. The cost of building under a body of water, which is large, does not make most of the ticket price difference.
The cost of the Channel Tunnel (by car) is determined by what the market will sustain: the only alternative to move a vehicle is a ferry. The train is a bit faster.
A more realistic comparison is something like Villach in Austria to Edirne in Turkey, which is 1400km by road, and €259 one-way for a car plus €149 for one person (https://www.seat61.com/motorail-trains.htm).
For comparison, math for the Villach to Edirne trip comes up with USD 158 in gas for the average US car mileage and gas price for 1400km, versus USD 443 for the car + person tickets.
I'd gladly pay 300 dollars not to drive 1400km. Once or twice a year, I drive 320km, and I think about twice that (to and fro) is the limit of what I am reasonably willing to drive over a couple of days.
In my own little world, I don't worry too much about 1400km in one day. I'll probably stop and take a long break at some point (and maybe catch a nap), but I don't think I'd be willing to pay $300 to avoid the drive.
It's a long day of driving, but I enjoy the diversions on trips like that. There's a whole world of stuff between A and B and it's nice to be able to stop and take some of it in whenever I feel like it when driving alone, which I can't do with a train that has my car loaded on it. (My solo driving style suits me very well.)
Or: With passengers, we can take turns driving and the cost per-head decreases instead of increasing.
1400km in Europe is significantly more taxing than in the USA. The density means more junctions, traffic, variations in speed etc -- I think it's twice the mental effort of the same distance in North America.
Depends on the roads, obviously, but my limit is around 12 hours a day, however far that gets you.
I’ve driven 680 km each way on interstates to my in-laws’ home. There on Friday, back on Sunday. Had to drive because I was bringing gifts, way too much for air travel.
And to most Americans, that’s not a particularly long drive. It’s all a matter of what you’re used to. I’ve done 4800 km in eight days and didn’t do anything but local driving on three of those days. That’s a bit more than Madrid to Berlin and back. It’s a lot of driving, but it’s definitely doable even if you’re not twenty years old.
Madrid to Berlin is not comparable to the same distance across the USA. The population density means the roads are much busier and have many more junctions etc.
With the average EU consumption (6.0L/100km) and the average price (€1.59) it's €133.
(Though for a journey this long people with multiple cars would probably be taking the larger one.)
The train costs more, but means families can play with their children (around a table) rather than having them stuck in the back seats for hours, and probably part or all of the journey is overnight.