What does 'water pump cap seized' refer to even? It only has these parts: A housing, a spindle, the bearings, seals to stop coolant entering the bearings, an impeller pressed onto the inside end of the spindle and a cap pressed onto the other end to bolt the pulley onto. The spindle is no longer rotating freely? Bearing is shot? The cap is pressed on, and not supposed to turn on the spindle, or the pulley would not drive the impeller.
It says the coolant leak is from the outlet gaskets at the top of the motor, where the radiator cap screws on. Not from the weep hole in the pump.
I have never seen a bearing fail before a seal. Is it possible? Usually you get lateral movement when the bearing is worn, not stiffness. This is the sign of wear. Stiffness is good. Means the seal is still tight and the bearings are not worn.
There is a little weep hole coolant comes out of to show the seal is gone, and that coolant is entering the bearing. There is no mention this is the case. This is the factory provided indicator it is time to change the pump.
Was it noisy? Trust me, nothing makes a bearing squeal like that red coolant, you only have to spill some on the idler pulley when filling the radiator to know that.
Chances are from the sound of things the pump is still OK. The dealers are money hungry. On the one hand, there is the argument that if the pump has been on there as long as the gaskets on your outlet which are leaking, the pump is aging, and maybe you should get the mechanic to change it while they are at it. Which would be a good idea if everything together cost you $100.
The owner can drive away, and won't be back at the dealership complaining the coolant system failed again in no time in the eventuality the pump does fail. The dealer can give the car back to a little old lady or fleet with the guarantee everything is good for a long time.
But they just use this as an excuse to change everything they can at the massively overcharged price you mentioned. They are not out to look after the customer. They are out to fleece them, and the customer's desire for peace of mind is their excuse.
Why fix it if it ain't broke, I say. Just change your outlet gaskets, and keep going till you see coolant coming out the pump weep hole.
You don't even have to change those gaskets on the outlet. Not that you would be shy of the $5 you need to do so. Just put a bead of gasket in their gallery, let it rubberise first, and the old gaskets will protrude again nicely when placed on top. You can put a tiny bead around the outer edge for good measure, but you don't want any excess that might detach and go into your radiator. The coolant system is best kept pristine to avoid blocking the radiator.
Which it will always be if you use Dex-Cool and distilled water, and prevent any dirt or gasket goo going in there.
There is a good use for used COVID masks. That tap at the bottom of the radiator is to let you keep your Dex-Cool, which lasts 5 years. You can use your old mask to filter the coolant every time you drain the radiator, before you put it back in there.
I put a tub under the tap. Drain the coolant into that. Then I get a big clean water bottle. Put the old mask on top of the bottle and use the ear rubbers to attach it. Pour it in. Even gets any oil slick out of the coolant if you were messy. That stuff is pristine to put back in there after that.