My wife just had to have one. Personally I preferred the rings. We found the best way to clean that stubborn area is to put some baking soda on it, pour some clorox, rub around with the basting brush and then put some paper towels on to keep it wet and evened on the spot for hour or so. Easy clean then. Might need to mist it to be sure it's entirely wet. As for the crack, not much you can do for it, other than replace the top. Very likely someone DID drop something on it but didn't tell you. When we had that 5.8 earthquake in Maryland, a crock pot fell off our cabinet top and hit our stove, but thankfully right on the metal rim edge, or we'd have been out a top also.
Ever since I saw flat stop stoves, I wanted one. I hated my old coil burner stove that would, on occasion, have a small fire under it from something that spilled on the foil. About 3 years ago, we were finally able to get a beautiful stove but after a few months, the gray circles around the burners started to get marks on them for no apparent reason. I tried every stove cleaner, including baking soda, vinegar, etc. and nothing worked. Then a little "fracture" mark showed up that looks like a rock hit it but nothing fell on it. Now the left front burner has a crack. I am so sad as I watch this get worse and worse. With my husband unable to work, we simply don't have the money to just get a new one. I spend hours a week cleaning it. I have to wipe it down with a sponge, use baking soda to get any cooked food off of it again, wipe it off again with a sponge and hope it looks a little better. So sad.