Not sure if it's just a German thing but they're very big into offering incentives to switch to them. For example, Commerzbank offer you fifty euro if you switch your current account to them (but I didn't get it at the time I opened my account because I was switching from an Irish current account due to moving here and that didn't count.
). I remember Irish banks doing similar, especially for student accounts - free mobile phones etc.
On the Commerzbank website they have a similar offer to the one you describe for people who switch their investments to their funds. 200 euro for 10,000 investment, 600 for a 50,000 investment and 1,000 for a 250,000 investment. It look like a fairly straightforward deal but these things tend to be a bit like supermarket BOGOF deals. Good on the surface but once you look at the small print, account costs (for example with the deal I looked at, setting the investment up over the phone costs 9.50, other costs for German investors were 0.25% of value invested, minimum 9.90), or minimum investment periods or whatever, you might not really end up making as big a gain as you think. Like BOGOFs, if you happen to have the money, don't get sucked into doing something you weren't prepared to do or already interesting in doing anyway, then there's nothing wrong with it. If you start thinking about doing something like borrowing the money to invest then it's just as silly as buying ten packets of something you never eat just because they were on special offer and too good to miss.
P.S. If anyone ever moves to Germany and wants to open a current account with Commerzbank, let me know. For a referral I'd get a 25 euro voucher and a free toaster