London to Paris or Brussels by Eurostar takes just over 2 hours - comparable to London-Manchester or London-Leeds journey times, and the distance as-the-crow-flies isn't that much further.
I think you've gotten your distances wrong. London to Manchester is around 186 miles (300 kilometres), compared to the LGV Nord in France which runs from Paris to Calais at 333 kilometres (207 miles). So the distance on one side of the channel is already greater, not including the 50 kilometres (31 miles) through the tunnel itself, nor the 108 kilometres (67 miles) from the tunnel portal to St. Pancras. Give or take a few you have a journey of about 186 miles from Euston to Manchester compared to a journey of 305 miles (490 kilometres) from London to Paris. To add to this, the stock with Eurostar is faster, and given that they run on designated high-speed tracks for the majority of their journey while the Pendolino runs on a mixed-traffic railway at a lower speed, I don't think it's a fair comparison.
If I try and book to travel the next day, the fares for a return journey limited to a particular train are eye-watering even by UK rail standards - sometimes up to £300ish for a return journey, even on a standard ticket (though it gets a lot cheaper and much more comparable with UK fares if I book weeks in a advance).
The whole point is to try and get people to book in advance really. I remember when Nick Hewer interviewed a manager at Virgin Trains, and apparently it's all done in an attempt to spread out the demand as best as they could. Not sure how well it would apply to Eurostar in this case, but still.
A very few trains stop at Calais, which at an hour out from London ought to be commutable (at least before Brexit), yet there seems to have been absolutely zero attempt to tempt anyone to use Eurostar to commute (in contrast to the SouthEastern HS2 trains which travel a similar distance and rely on commuters). Yes, I realise there wouldn't be a huge Calais-London commuter market, but if it was promoted, there'd be some market, which would add to the numbers on trains.
Some potential market doesn't sound promising, especially if the market isn't really, and wouldn't really be huge. Eurostar wasn't really set up as a commuter service either, it was really more of an international railway transport link connecting major European cities. It is also an open-access operator, and such it doesn't really have any commitments to government to provide commuter services, which it won't so long as there isn't the demand there. Southeastern on the other hand does have franchise commitments and is a commuter TOC. In regards to similar distance covered, again I think you just have to look at how far each train travels on a single journey. Class 395s cover less distance than 373s/4s in a single run.
Then there's what look to me like absurd check-in times, when you'd have thought all you basically have to do is show your passport, have a baggage check, and jump on the train: According to the website, 30 minutes unless you 'buy' a shorter time by getting an ultra-expensive Business Premier ticket.
International transport procedure. Nothing unusual there, and in fact when I travelled Eurostar I found it to be very reasonable check-in time. With 900 potential passengers I'd say it was great in fact. I'd much rather check in for them than for a plane. Just think about it too, is thirty minutes really a long time?
This all gives me the impression of a company that's doing its utmost to put people off from using its trains. Indeed a good part of why I've never travelled on Eurostar - is that it looks to me such a hassle and so expensive in comparison to any UK train. Is my impression unreasonable?
Yes, I'd say it's unreasonable, not for any complex reasons either, but just simple logic. Even if I am completely wrong on everything I have said and will say further, I can confidently say without doubt that Eurostar is not trying to put people off using it's trains. No company, private, public, state-owned etc., with any sense will try to put people off using it's products. I promise you, as someone whose used Eurostar, I would absolutely do it again. In fact, if I had to travel from Liverpool to Amsterdam, I'd prefer the train to the plane. So if they are trying to put people off using trains, they're doing a bad job at it.
It may look like a hassle, but I promise you that airline check-in is much worse than Eurostar, and it's prices compared to other TOCS probably seem more reasonable with it's operating cost. Eurostar trains are some of the most technologically advanced in the world, running over several different signalling systems. Not to mention, the labour costs are higher since Eurostar drivers are the highest paid in the country, since they're expected to know the rule book of several countries along with being multilingual. That's just one role too, but the point is made that Eurostar might be as expensive as some local TOCs, but it's got more to deal with in some ways too. No other TOC runs over international borders, something that Eurostar does every day.
EDIT: Okay I realise now that the OP originally said "as the crow flies" to mention the distance between London and Paris. In actually it says London to Paris is 344 kilometres (214 miles) and London to Manchester is 262 kilometres (162 miles). But having said that, using the "as the crow flies" method is still not really a fair method given trains don't travel in that direction and often times do deviate from a straight course. For a start, the LGV Nord takes a big cutting corner at Lille and such, so I don't think measuring in a crow flies method is fair for any rail travel distances.