250TB/month is about 770 Mbps sustained. And you still only get a strongly worded letter!
Relevant xkcd: https://xkcd.com/1499/
You cannot fill up your car's tank with soda at a "free refills" place, neither can you camp and eat 24/7 inside an "all-you-can-eat" buffet.
I don't think it's unreasonable to still call those services "unlimited" and let the restaurant/internet provider decide when to drop a customer that they don't want in their premises/on their infrastructure...
If the restaurant sold 'Unlimited Soda, 2 liters per minute, £50/month' I would expect them to deliver on the very specific quantities they promised at the price they offered. If they tell me I'm over-dispensing, I think I'd be rightfully annoyed that they have over-promised.
Instead, Hetzner sells "unlimited bandwidth" the same way McDonalds sells "free refills". It's also understandably unreasonable for someone to start pushing data at the max rate for months non-stop, the same way it is unreasonable for people to fill 50 large cups with soda.
If people have accepted the "...within reason" argument for free refills and all-you-can-eat buffets, why not also accept it for data usage?
False Advertising. Simple as.
And even if you were right, even if it's just a case of false advertising and the provider wanting to get out, there is nothing wrong (neither morally nor legally) for them to unilaterally terminate the contract, which they could have well done instead of writing that notification letter. They explicitly state this in their TOS. Most companies can still (luckily) decide which customers they serve and which they don't
(If you're really lucky, you might be able to get 900Mbps or so, but that's not likely: the max throughput on 1Gb Ethernet is below 950Mbps, even if you had packets flowing continuously!)
They also said the use averages above 250TB.
It averages on multiple of their servers, which indicates to me that the average was taken over the course of some months (?). They may well have reached 320TB in some months on some servers.
I'm not surprised by this. For me, unlimited traffic (with 1 gbps) means i can spike in some months without having to worry about costs exploding, but if I'm maxing it out consistently, then I might be asked to move to a different service or upgrade.