1) Safety. Your wallet isn't worth a knife in the gut.
It's not about the worth of the money, it's the principle of your actions. Muggers aren't of the mindset to be deterred by "Take whatever you want, don't kill me!". That's just confirming your own weakness and exploitablity to them. It's true, they want your money, not your life. They certainly don't want to risk their own necks either. What acts as a deterrent to someone of that mindset is leading them to believe that targeting you, or continuing to target you, will not only have a lesser chance of actually obtaining your money but a higher chance of sustaining harm themselves in the process. Poisonous butterflies are bright yellow and orange to tell birds that they'll face harm if they consume them, walking around with a pistol on your belt tells muggers that they'll face harm if they try to mug you. But that's just posturing. If you choose not to be a victim, if someone does decide to push, you have to push back.
2) Eliminating their reason to commit a crime is more effective in stopping the practice on a large scale.
Agreed, but we aren't talking about the large scale.
Pretty much all theft is motivated by desperation.
Some theft is motivated by desperation. Other thefts are motivated by greed, and some are motivated by the influence of criminal culture.
Taking people's stuff has a huge deterrent attached, from both the risk involved, and the fact most people aren't heartless sociopaths.
Sidenote: Sociopathy is no longer a term used by the psychological community. What was previously called Sociopathy has been reorganized into Antisocial Personality Disorder. Also, in this discussion, psychopath would be a more accurate phrase for what we are referencing.
Psychologically, thieves justify their actions along two broad pathways. Psychopaths are naturally unconcerned with others and see their actions as self-justified. From their view, if someone else has something the psychopath desires, they are morally wrong for keeping it from the psychopath and the psychopath is morally right for claiming what they want. These individuals are particularly dangerous, even if they are not committing crimes.
The psychologically "healthy", on the other hand, justify their actions through depersonalization and rationalization. They do everything in their power to see their victims as not being people like they themselves are, and rationalize through the possible need they have for another's possessions.
So, giving them reasonable recourse to get what they need will mean theft is a bigger hassle than getting it the "normal" way.
This is true on a societal level, but not on a personal one. The former will decrease crime because it gives the desperate thieves an out, the latter will increase it because it tells them all that people won't stand up to them.