The more successful people who admit their past weaknesses, the less shameful it becomes. Having 150+ rejections shouldn't be a problem. The problem is the person (who? me) too scared to do those 15 or 150 applications in the first place.
[1] Application but no offer
You have to approach your job search as if it were a sales funnel, focusing on optimizing those things within your control. Those factors are number of applications, quality of your application materials and portfolio, and actual interviewing skill. You can't easily influence whether somebody takes the time to read your resume, which is why I don't think it's a bad sign that he had to send out 150 apps as a person without a strong professional network in the area. As far as I'm concerned, the real process begins when a recruiter sets up the first informational phone call. I'd be much more concerned if I found myself frequently flaming out at various levels of the process after I actually have a company's attention. Converting those warm leads into job offers is where raw interviewing skill comes into play. Some people, like the OP, just need a little practice to get good and comfortable at it.
No shame in needing some practice at those things that frequently come up in interviews but actually have very little to do with the day-to-day working life of a software engineer.
From personal experience applying to jobs as a soon to be graduate, I know many of my friends with similar qualifications didn't even receive an interview at certain companies, even though I know they would do well in them from work we've done together previously. It's also interesting that I received interviews with all of the top companies I was interested in, but I didn't even hear back from several that I would consider the next tier down.
Even better, when I was applying for internships last year, some companies sent me rejection emails in the middle of the summer, seemingly indicating my application was unearthed in the abyss of the job portal by some random happenstance.
As I said, fickle.