I have a Thermador "Professional" 48" cooktop with a grill and a griddle. I use the griddle all the time, just like others said, its a small flattop, without quite as much horsepower.
For eggs, I bought some egg rings with little wooden handles on them. A little oil on the griddle, and I plop down the rings (to let them start to heat up) and then I generally use a fork and quickly whip the egg with lots of fresh black pepper and pinch of salt. What I really like about the egg rings is that the egg stays in place, and it is even thickness from edge to edge and all the way through, so when it is finished cooking, it is highly uniform.
After a while, you get the hang of the rings, and you can gently pull them off, and place them somewhere else on the griddle and do some more eggs. It takes a bit of time and practice to know when you can flip the ringless egg, without it losing its nice round disk like shape, but once you get the hang of it, its great.
Wouldn't be without it. And I leave the patina on the griddle, even though I do scrape it down to clean it, and then add some fresh oil to keep it (Stainless Steel, not Titanium like more modern ones) from rusting.
I really can't say that I notice any flavor problems from the previous cooking session, but I think its like a cast iron skillet that has been properly seasoned. It doesn't seem to pick up flavors either.
Anyway, thats my experience. On the other hand, when I used to cook, I remember those smelly volcanic bricks and having to scrape the flat top spotless, and then having to grab the long scrap oil pan in the back, and it would always drip onto my nice cleaned surface!