When looking to run long distances Eurostar is crippled by the immigration and security constraints it has to operate under.
Any other long-distance operation, international or otherwise, survives on a combination of end-to-end journeys and passengers boarding/alighting at intermediate stations. Thus there may be a journey of five or six hours or even longer, not too many people will be on board for all of it but it can still be quite well used over most of its length. Cross Country is the classic UK example and there are no doubt many others across Europe.
With Eurostar it is extemely difficult to do this, because of the risk of either people without documentation finding their way into the UK or explosive devices finding their way into the Tunnel. Either a UK border post and security screening needs to be set up at every boarding station, or everyone has to alight at somewhere like Lille or Brussels with their baggage to undergo screening and re-join the same or a later train. Either is very inefficient use of officials for what will probably only be a handful of services per day, and is no doubt charged to the operator concerned. This also means that short-distance passengers can't be carried on the UK-bound leg unless either they are required to submit to the same document and baggage checks, or a portion of the train is dedicated for them and segregated appropriately. In the latter case the portion must run empty on the final leg into the UK, unless it is searched at the last stop and declared "clean" before re-boarding - which also results in a long stop and in passengers from the intermediate stops to the UK having to alight and re-board.
It's possible that screening will become more widespread for European high speed rail in which case Eurostar could share the facilities with other operators (but would still have to pay for the immigration checks, unless the competing operator served the UK too). However this would build in a check-in time to a wide range of rail journeys, reducing competitiveness against air in general with, I believe, virtually no benefit to public safety.
With Brexit-related uncertainty, which could lead to the imposition of customs checks on top of all this, it would be a brave operator who committed significant resources to service between the UK and more distant European destinations at present. The Eurostar Amsterdam service would appear also to be providing extra trains to/from Brussels at peak business times, so the extra cost of running them to/from Amsterdam is relatively low. I suspect they will disappear quite quickly if Amsterdam patronage falls short or Brexit makes operation more onerous.
Edited by Edwin_m, 25 February 2018 - 16:21 .