There are "other ways" to do things, some of which work - but the fact that they work does not mean they are the better way to do it! Noting Lycoming's own remark about the primer being the "best" method to start their engines.
Light aircraft are subject to many variables which are very difficult and sometimes impossible to pin down but they dominate. The fueling systems are very basic and crude. The pilot therefore must use some initiative in managing the fuel for starting. It is possible to operate large aircraft exactly in accordance with its flip charts and the maintenance regime is very detailed. Fuel flows for instance can be measured precisely. However an over rich turbine engine can cause havoc just the same as our basic pistons; some years ago a heavy jet was cleared to start. My C150 was parked at the approved Avgas fueling point and being fueled from a Bowser. The distance from the MD80 was of over 80 metres.. The MD80 had failed to start and air traffic reported to the pilots that they had observed a lot of black smoke. The captain in spite of this continued to a second attempt. Apparently the flame from the engine was spectacular, my C150 was launched into the air, flipped 180 degrees and its port wing struck the Bowser on landing inverted. Fortunately the fueler had finished and replaced the fuel cap and he was able to jump clear. There was no fire, thank god. Two very shaken refuelers and my C150 written off.
Even without the POHs, I have seen 150s where the fuel was literally dripping from the air box. Students who couldn't get the engine started on a cold day were prone to forgetting the briefing and just priming a bit more... and a bit more.... etc.
It is not the method that is always the hazard rather it is simple common sense. If an engine does not start as it should then clear the engine of the excess fuel that WILL be present. It is unlikely that you will be certain of why it did not start.- and only then start again. Have in your mind that the failure to start may well be an over priming rather than too little. By clearing the engine you will not be at risk.
Pilot DAR, you reported over priming
with the installed primer when you had your engine fire! From the facts that you reported shouldn't you have cleared the engine of fuel and then attempted a second start?