There may be a small sight glass, but more than often you cannot see the pilot flame through this.
There may be another viewing port, but likely it is far from the control unit, and it is not easy to be there at the right moment to see what is happening.
The BMS is often not showing you exactly what is happening either. A "No Flame" lockout does not tell you if the pilot got blown out or the pilot lit off, but the flame rod is dirty and everything shut down. Many things could have caused this situation.
Your regular servicing will help. Like with a doctor, it is better diagnosed by someone that has intimate knowledge of the system. Having said that, sometimes you just need a fresh set of eyes. If you cannot get a diagnosis, get some more opinions.
It can be frustrating when a burner does not light off. Like when the car doesn't start, you cannot see why. Unlike a car, you cannot just pop the bonnet and start tinkering. There are large delays whilst you go through the pre purge, rearrange operators, and communicate what is going to happen next. There may be extra tradesmen to bring in, SWMS to be redone, etc.
The best thing is to ensure you service frequently, & have good support for all your equipment. It will not prevent you having anything go awry, but at least it will get you back on track with less downtime & concern.