Yes Ketchup does go well with eggs.
I always put Ketchup on my eggs to add some flavor to them which makes them taste better.
A friend of mine in school years ago in elementary school was putting Ketchup on his eggs and I tried it myself and it was and is delicious with Ketchup on Eggs.
I also love to sometimes use Hot Sauces on my eggs which also makes the eggs taste better when I'm in the spicy mood.