This is very well articulated. I have definitely tried this before and it works like a charm. However, you do have to be careful about who you try this with though. Long term satisfied customers, customers in urgent deadlines and ones who are generally reasonable about costs value this sort of a pricing/engagement.

I have seen that a bigger benefit from this sort of a pricing model is a stronger relationship that develops with customers who come back to you time and again.

Another thing I have done in the past (ours was not really a services business but a niche solution business) is defined the pricing and after discussing with the customer that it doesn’t fit with their current quarters budget, I agreed to discount it to “make it happen” and they greatly respected that. And then made up for it the next quarter.

I would highly recommend it, but you need to know "how" to do it right. You should not come across as casual or clueless in doing so.