To your point [1]
reputation has little if at all relevance here.
The US largely employed a strategy of asymmetrical, anti-access, area-denial. shock and awe etc... in Iraq initial phase of the war.
put simply, we see you on the field we turn you into vapor, essentially making open conflict with US forces a suicidal idea, because you can never match the fire power.
This strategy, and not the reputation you talk about, is what encourages the enemy to fight an attrition, largely non kinetic war, over a long time, its simply a prudent logical approach to a fight against an enemy with far superior capabilities on the field
Parts of the military recognized this, and hence the COIN doctrine was born, wining the battle is easy for the US military, it is done swiftly. wining security post conflict (re occupation) is something the US military had consistent problems with primarily due to the size and nature of the occupying forces (20 something marines make a very effective combat solider, but lousy and impatient occupier)
Another way of putting it, is that the US does not need a great number of troops to win armed conflict scenarios, but require a great number of troops (of a different sort) to secure occupation, this was the point that general Eric Shinseki made at the time before congress, and was ridiculed for it by the neocon know it alls.
I do agree with you that the US will continue to have an increasing number of low level armed conflicts around the world, It is the fist of globalization if you will.