The router CAN cause problem, but everyone's problems may be different. Rather than letting the customer decide whether the router has anything to do with the problem, the router needs to be taken out of the equation for the testing. The same testing across the board. Short of sending a tech to everyone's home that is having a problem to determine what is involved in that problem, which would be a ridiculous and costly endeavor, there needs to be a universal, simple method of testing that applies to everyone, regardless of what one has or one thinks is causing the problem. It's as simple as that.
I'm not arguing with your situation, only the statement about the router not possibly being part of the problem. The problem is that you are piggybacking on a conversation of a problem that has nothing to do with yours, so your interjecting YOUR situation into theirs can only add to the OP's, and anyone else that is reading this thread's, confusion. Because of this, someone might take your statement about the router as a blanket statement. You were replying to an answer about the routers, yet interjecting YOUR experience into it, as if the answer was given to a post by you, which is wasn't.
Your problem is singular to you. The fact is, routers need to be taken out of the equation when it's requested of people to do some speed testing. it's as simple as that.
As a point of clarification for others that may read this, QoS is a "traffic shaping" function that is available in several different forms and known by different names depending on router brand.
It can be used to "prioritize" certain activities. It is very possible for a given activity (a speed test?) to be given a lower bandwidth priority at certain times or under certain conditions ... a scheduled task starts up, a higher priority background process is triggered or a second device is turned on and joins the network and thereby shares in the available bandwidth.
Reducing the number of variables to the absolute minimum during initial troubleshooting is simply a very good practice.
QoS is not the only router function that can have an affect on performance. Cloud based router "services" can also slow performance if the requested data is not in the routers internal database, then the router is forced to access an external server ... that takes time.
There are many more reasons.
First rule of thumb when troubleshooting ... simplify the network, reduce the number of variables.
Just out of curiosity, why did you purchase a new router? Was there an indication that there was something wrong with the old one?