I believe that the pro's of this would be that a website can do way more than ingame.
The website could calculate all sort of percentages, percentages won, K/D ratio, times you won without an egg (if there's a database for that), how many eggs you've broken (once again, if there's a database), it could maybe even calculate how many points you've spent in total, and on what sort of abilities and kits, percentage of points spent on what games, and some overall stats. This could be really satisfying to take a look at, and not everyone needs this, but I believe a lot of people would use this if the possibility is there.
Then again I've seen some concerns about people saying that the contra's weigh way more in.
People are concerned about the negativity, the bullying that might follow because everyones stats are open. I'd say this is something that is possible, but not something I'm expecting to happen. By now, a lot of people are grown into the community and everyone knows "That person isn't that good", or "Avoid him, he's too tryhard". So stuff like this is already being said, I don't believe that adding an online statistics tracker could go any worse. However I do agree with you, that there still is a possibility that this could happen.
However I do not think that this should change the fact that having a website with your own, and everyone elses stats, would be very fun to look at!
After all I want to say, this is something I didn't know I wanted myself, and now I do!