I have a Whirlpool Gold refrigerator about eight years old. The water dispenser runs water in a glass for a few seconds normally but then runs slow. Note that it doesn't slow down. It's an immediate switch to slow dispensing after about 2oz of water is dispensed.
I think (I think) this started after replacing the filter a couple of months back. I believe I was to fill the filter with water and let it sit for a while (or somesuch) but forgot to do that and just installed it. I'm wondering if that may have caused an issue in the filter to make it clog after a few seconds.
I would replace the filter to find out but I don't have one.