KLM Flying Dutchman - Online check-in problems when flying to the United States (I have a visa)

Whenever I try to fly to the United States from Amsterdam (delta flight, but you check in with KLM or on the KLM website), I can't manage to check in online and I always have to go to the check in desk. I have the same problem at the kiosks. I think the problem is that I have a student visa, and don't have an ESTA (because I don't use the visa waiver program). This is kind of annoying because I have to come to the airport early to check in. Does anyone know what I can do to be able to check in online?

Without ESTA you cannot check in online, because an agent will need to check your passport for the visa. From the KLM website (https://www.klm.com/travel/nl_en/prepare_for_travel/travel_planning/usa/esta.htm) :

"If you have a valid visa for travel to the United States, you can still use it for the purpose for which it was issued. You will not need an ESTA travel authorisation until your visa expires. However, if you wish to check in online at KLM.com, you need to have ESTA travel authorisation as well. Otherwise, you can check in at the airport."

However, I have a work visa and was advised against applying for ESTA travel authorization by my employer. Perhaps with a student visa it is not a problem, but I would check with the US Embassy or your US University first.

Last year I had both an ESTA and a Student Visa, was no problem. But ESTA is not really required if you have a Visa. Just check in with an agent at the desk.

I've not travelled to the US with KLM/Delta in many years, but other airlines ask (as part of the API/check-in process) if you have a visa - so at least they allow an alternate route than the ESTA one (though not having ever had a US visa, I don't know if this just amounts to a statement that you have to see a check-in agent. Flying to the US, they generally want to see you in advance - or at least in Heathrow, everyone has to answer questions from an ICTS official before travel). I suppose, from what you've said, that KLM.com does not allow you to indicate that you have a visa?