You might be able to get away with that in England or British Columbia, or Thailand

That's a little unfair... I have operated in very low temperatures and I have frequently been asked to help my fellow aviators start their engines in very low temps.
I've usually been successful with only a few frustrations.

As for the idle jet and starting with the throttle closed, I use this technique for engines that are already hot and it usually works. In this way I avoid flooding the engine. With a hot engine you can never be certain of your start point, do I need to prime?
Primed might mean flooded, so let's try simple first.

Sometimes I'll give the throttle one pump with a warm engine and an accelerator pump before using the starter. But never more than one as noted above, in cold weather you risk pooling the fuel, in both cold and warm weather you risk flooding.
If I only have the accelerator pump, in cold weather I'll pump once and suck in twice by hand each time. In this way each prime using the throttle is drawn straight into the cylinders by hand.
There's also no ignition source to spark the mixture, backfire, and cause a fire in the carb box or worse.

All propellers are supposed to be fitted in a position for swinging, but some mechanics don't like hand propping and deliberately put it in the wrong position.
The Cherokee's maintenance manuals specify the correct position and so in this type at least the mechanics are counter to the manufacturer's requirements.
The problem is that we have to turn props by hand from time to time and mechanic's opinions can lead to highly dangerous situations.
The Warrior would not start, I wasn't there at the beginning otherwise she would have started.
I helped them out, but the propeller was in the wrong position, and so I had to be doubly careful how I turned it.
The aeroplane did not fly that day... With the prop in the correct position it might have, Michael would have swung it!
Imagine that aeroplane being stuck somewhere and a desperate pilot trying to swing a wrongly positioned propeller with the greater risk of serious injury...

I thought that the position of the prop was for engine balance. Usually with the dowel pins it is almost impossible to put it on another way, but you are right, the 10 o'clock position is perfect for hand bombing.

Warm engine starting at idle usually works, but not when cold I find. For fuel injected engines I usually start at idle and gradually open when cranking so at some point there will be a perfect mixture of fuel (without the accelerator pump screwing things up like in a carb-equipped engine).

All engines have their foibles...

The IO-240 is a bugger to start at the best of times and yet the more powerful carburettor equipped Roll Royce O-240 was easy to start.
I know we're in for a big bill at some time with this hard to start much abused engine... There's also all the ground running time with maintenance trying to make that ill founded injection system work. It still does not work well... Give me a carburettor please!

The IO-360 in the DA40 is easy to start even when hot while it's carburetted version was a bugger hot!

The 0-200, C90, C85 series are the easiest starting engines ever, as long as you don't prime when hot.
These engines I start from throttle idle when they are hot and this works well.

The 0-235 likewise likes throttle closed and no prime when hot.
When cold this engine starts easily if you prime and suck, prime and suck, prime and suck four or five times before touching the starter.
I watch people crank these engines over and over while the battery dies. Sometimes the prime catches fire all down the nose leg, and I have seen the air filters burned away.
I do what I do, get in and she's running within two turns of the starter motor, so what's the best method?

Treat the propeller live, ensure mixture ICO, mags off, throttle closed, chocks in, competent person in cockpit, and check these items twice before turning by hand.

BTW there's no peg on the Cherokee's O-320... My brother put the propeller into what he'd heard was the smooth position. I wouldn't swing it. It's in the maintenance manual position now which is the correct position for swinging.
I see no difference to the smoothness, it still feels like a John Deere perhaps.

For many aircraft engines, if they are not starting easily there are fundamental problems.
Check the setup of carb/injector, and especially the timing.
When were the mags checked last?
500 hours? 5 years?
Besides that IO-240 I know of no engines that could not be started with reasonable effort.

I had trouble swinging Pitts propellers... Philip Meeson would come in, everyone friendly, then when he was leaving the place would suddenly be empty and Michael would be left with the hard job of swinging his prop
This was timing... Sometimes the mags are set too far advanced, better fo power at high revs, but bad for starting.

I had trouble swinging Pitts propellers

Try a 3-blade claw, with sharp trailing edges, on
a high-compression AEIO-540 sometime

A friend of mine had his four-cylinder 200hp AEIO-360
starter die in his S-1T at a contest, years ago. The
tea and crumpets contest crowd quite specifically did
NOT approve of my hand-propping him. Amongst
other things. But, with it's two-blade metal prop,
and his expert priming, it was a cinch.