The Fritzbox 6591 uses an Intel Puma 7 SoC. The Puma 6 and Puma 7 both have latency issues due to defects at the hardware level. Intel issued some firmware updates to mitigate the issue, but it was not fully resolved. The general consensus seems to be the Puma 6 still has problems no matter what, but if a Puma 7 device can be put into bridge mode to take routing load off the CPU, its performance as a modem only device is reported to be acceptable.
If you can put the Fritzbox in bridge mode, you have nothing to lose by trying before you buy your own ISP compatible modem.
It also depends on how inexpensive used modems are on ebay in your area. I was able to pick up a used 24x8 Motorola MB7621 DOCSIS 3.0 on ebay for so little it was essentially free. That may not be the case where you live.