@juliank Since August 2016 it has been your choice whether to rely on your ISP's modem/router or not. I switched on day 1 and never regretted it.
Also, I disagree with the statement that you'd be on your own when having connectivity issues. Sure, ISP support people may tell you it's your fault but let's be frank: it's almost never the router and they know it ;)
As said, separate modems would be cool. At least, used Fritzboxes are not that expensive.