Having been in a similar situation in a much larger delay sequence ATC won't care what you say until you get to the "mayday fuel" call. Luckily we had options to reduce fuel flow dramatically, position for diversion and landed with 50 minutes fuel after the sequence freed up, the original delay had put us within 5 minutes of minimum. When we told them we could not absorb any further delay they were just interested in where we were going to divert to. Our situation was fine until an aircraft behind declared a medical and added the extra delay time, always good to have at least another 15 minutes spare for those sort of occurrence.
And that’s going to be ATC’s get out of jail free card. If they didn’t declare minimum fuel and given a time then it will be on the pilots.
ATC already has a get out of jail card, holding requirements were changed from holding fuel requirements for traffic to 'expected traffic delays', which means the holding fuel requirement is subject to discussion, I take that amount as the minimum expected delay and add some more if I think it's under-cooked. Like if you hold a nearby controlled airport as an alternate, the expected delays are for expected normal traffic, so if you divert there on short notice a short distance expect more delays due to unexpected sequence changes.