The thing is I don't think if you don't work out the nerves about approaching women that you won't even talk to a nice girl on the way to work. You'll just stay in your shell. However, if you are used to talking to girls like that, then it's an easier stretch to do that if you see someone on your way to work. If you don't cold approach because you feel desperate, then in that example of meeting someone on your way to work the desperate vibes will still come out because those vibes are based on how many hard options or positive experiences you've actually have, not on how or when you are approaching.You realize you can go out with the express purpose of meeting women, while not being a "PUA" right? This is a primary point I keep trying to make and it's just not sinking in for some people.
PUA: Mystery. Peacocking. Dancing monkey trying to entertain women and say whatever needs to be said to "create" attraction in them.
Normal, but enlightened Person: In daily life, and sometimes with the sole intent, goes out on a walk and enjoys interacting with strangers. If he sees someone he is attracted to, he will stop her and have a genuine interaction with her and if she qualifies herself to him, he will ask her out on a date.
If you are waiting in the subway and see a hot girl, you are allowed to talk to her. Shocking I know! And flirt with her. And ask her for her number. And ask her out on a date. 999/1000 won't immediately reach into their purse and spray you in the face with mace (I'm still waiting for that #1000). And if you are allowed to do all this while on your way to work, there is no difference in going out with the sole intent to do it. I've seen people argue that this will cause you to reek of desperation that girls will smell on you but I've not experienced this myself. My guess would be that the guys who are saying that are either too afraid to cold approach so they are making excuses, or they don't know how to hold a conversation like a man with a stranger they are interested in sleeping with so they had some bad experiences and rather than working to improve themselves, they simply throw out the excuse that it's "not a viable option."
Either way, if you go out there with the sole purpose of talking to girls then that's like molting or like a snake shedding its skin and makes it easier to talk to women because you are working on the anxieties and phobias. Now, if you take this medication known as "Propranolol Hydrochloride" 40 mg after cold approaching, it should work on the brain to relieve the phobia/nerves aspect of cold approaching, so that during consolidation (i.e. how your brain assorts memories after you sleep), if you cold approach the NEXT day in this treatment, then I think that should work at making it easier to work on the mind to cold approach.