A very rare situation for KLM and Skyteam.
It seems pretty clear that much of the assistance could have been generated in Bham, buy putting you on the BA flight perhaps to AMS, if they were available. This would be the station Manager’s responsibility in B’ham.
KLM do have only one flight to some destinations per day, with AF perhaps having more, or an alternative time. At times when i have been on the late morning flight from LHR – AMS with 60+ passengers connecting, it is 75% delayed due top LHr gate, runway, wna delay problems often up to or over an hr.
The crew go round the flights to individuals, detailing their flights, and at the end they announce which flight connections will be possible and which will not. Passengers have already been booked onto the next option possible.
I only had this problem once with KLM coming in from HKG where the KLM flight was delayed 6hrs +, and they booked me on to LH. Grotty old 747, and poor service, so I wish i and waited.
Recently i received an email and text, for delays from LCY from KLM informing me an hr before it was announced in the airport, that my delayed flight would be cancelled. I was re-booked automatically onto the first flight out they could confirm. No announcements were made at the airport for over an Hr (City Jet / AF), but i told them and it was in their system. I collected my own new Boarding pass an hr before the rush of 130 others started to queue!
I would certainly trust KLM more than AF.
But in my experience this is rare with KLM.
Baggage is some of the most reliable in the EU and efficient in Schiphol in the 18 yrs i have flown through.
But they did what was within their parameters to do, even being honest about their grid system.
You will get your compensation, but really this could have happened with any Airline, especially those from other EU gateways that operate daily only, which may include SQ, MH CX.
Some Business cabins are so booked out these days it is not always possible to overflow passengers from other flights.
As many mentioned on here, KLM are some of the best when it comes to Service. If you also lodged a complaint, you will find extra miles or an MCO coming your way also I am sure, and a phone call within a few days. Your processing of the compensation would be prioritised.
Air Travel is not always smooth, and we all have to anticipate this. I always arrive a day early, so even if this happens, it is taken into account, especially on multi leg / Airline trips as far as Australia and back..