There are two major economic problems that constrain device availability. First, companies pay huge performance penalties for having stock on hand too long (especially at the end of quarters) so no one wants to order an impossible amount and then hope they'll sell in the next 6 months; they try to order enough to meet initial demand (i.e. first week) plus perhaps 10% (to cover them while they order more based on sales) and if the phone outperforms expectations then they are short for a while (and remember Android is looking at over 500% growth year over year, so it's easy to underestimate).
Second, the amount on hand is related to how many units can be produced each day, and that involves the size of your assembly plant. That's a large investment, and companies can't create manufacturing solutions that produce based on the first weeks supply...otherwise the assembly line would hardly be running in 6-8 months, and there would be a huge money sink (which means they'd end up having to charge more for the phone). Instead they try to build the assembly line around expected demand, with a bit of flexibility to ramp up or down (but that's a pretty finite amount of flexibility). To get the higher initial demand they try to get the line cranking out handsets for a couple of weeks ahead of time, so there are more on hand the first week then there will be any other week.
But of course things go wrong when you are opening up a manufacturing line (especially for a totally new product) and where you might have planned for 5 weeks of production, problems in test units, or simple hardware or design flaws in the assembly line itself can easily shave a week or two off that lead time, which could cut first day availability by 20-30%.
So there's a ton that can go wrong, and even if it all goes right a really successful phone will almost always exceed expectations (and honestly, even if you hit expectations perfectly...supply will still be tight at first, because a line can only be run for so many hours in a day to increase the number of units being produced).
It's not Verizon or anyone else trying to screw us, it's just the realities of todays rapid design and turnaround environment coupled with the economic constraints of bringing gigantic factory lines up to speed at a price everyone can afford.