Advisors: Can you build a book exponentially faster by undercutting on price?

Possibly but this is a terrible idea. Why? Because your model would be commoditizing your practice and adding to the "race to the bottom". The reality of PWM is you do a lot more than just collect / manage assets. You have to. Your clients demand it of you. They want to know lots of stuff. They want you to jump on things whenever they want. Yet the only way you're paid is a percentage of the assets. You'll still have to do all these other things but you won't be getting paid enough. Also, and this is key, if they come to you for low fees, they'll leave you for lower fees. Price is not an indicator of value.

Do an exercise. Look at all the things you would typically do for a client. Advise on overall finance, goal setting conversations, mapping assets to goals, discussing taxes, retirement planning, income planning, succession planning, wealth transfer planning, being a resource for legal and accounting work - professional network, oh yeah and actually managing the money, etc. Assign a value to each of these. You'll find there's not much left to do anything with your suggested model. But you'll still have to do it.

In addition to being an FA, I'm a Principal and supervise many FAs. Had one with a decent book who used to do the discount thing. He just wasn't confident enough to charge what he should. Not only did he discount, he provided more service than anyone I've known. Was also a registered agent so would actually do client tax returns as part of his service. His thought was , "I do all this for them and charge less than everyone, how could they ever leave me..." He had quite a bit of attrition in the book because they just didn't value his service. I used to argue with him he should be charging more than the other guys, not less, but certainly no discount. He eventually started raising his fees on new clients. Unless you're dealing with UHNW, and probably even if, the fee battle is mostly between your own ears. 

At the end of the day, charge what you think you're worth. If that's too much for the prospect, NEXT! Your price is your price. If you have trouble closing business, assuming you're in line with the market, evaluate how you're communicating your value. That's likely the problem. They don't get to go the the attorney or CPA or doctor or dentist and say I'll only pay $1000. The attorney would say, "then you only get half a will".