Dropping Internet connections which are fixed by a restart sounds to me like a marginal connection (the restart forces a re-learn of DSL parameters). The Fritz box should be able to diagnose that.
And no, you're not forced to use them, "Routerzwang" hasn't been a thing in almost a decade, ISPs are required to allow you to use any router you like.
With Kabel Deutschland the process was also painless. I disconnected their box which they lend to you for free (also not avm), connected the fritzbox I bought on ebay and ended up on some form of captive portal where I had to enter my customer information and boom I was online. I've yet to encounter an isp which tries to force you to use a fritzbox. But then again I wouldn't mind since they are reliable and stable. :)