What makes a particular platform suitable or unsuitable for production use?
Yikes!  Either you're thoroughly confused, or your idea of production is different from mine.  I consider production to mean selling a product to the general public in quantities of thousands or more, then supporting and updating the design.  Products which don't go to the general public are either internal or contract work, and products which sell in smaller quantities are special-purpose or otherwise different. 'Several boards from Sparkfun' wouldn't fulfill a production need.

First, the cost of goods is always a significant factor.  Just how significant it is may differ from product to product, and it may be less significant if the particular item is only a small component of a larger system which has been optimized for cost. However, in any environment where you're in competition with other producers (which you must be because if you're in government or have a monopoly you wouldn't be asking this question), cost will be a factor.  The $35 for the Netduino (in cost alone) could usually be reduced to $10 or less for most applications with a custom design.  If you are convinced that the cost doesn't matter, there are further reasons against buying such a design.

Yes, all three boards were designed for students, designers, and hobbyists.  They are designed to be reliable enough for a development kit which sits on a desk.  That student should know a few things about safe handling procedures which the general population does not know or practice.  Issues such as ESD, long-term power dissipation, and component derating were likely demoted below things which are less important for production like solderability and simplicity. 

Your affinity for IDEs and prepackaged solutions is frightening.  In my opinion, you place way too much trust in your tool providers.  If the boards become more expensive, if the license terms are changed, if the server goes down, the software is declared obsolete, the board manufacturer goes out of business (etc. etc. etc...), your business is hosed.   Also, you lack an understanding of what's going on behind the scenes.  If something doesn't work the way the documentation says it should what is your plan? Your idea to buy a few Arduinos, program them, and deploy the product, for example, lacks any plan for code protection.  Someone else could copy your code out of the microcontroller, duplicate the relevant parts of the design for a third the price, and outsell you.
Relying on an IDE and language for the stuff you don't understand is a recipe for disaster.

Using a development kit in your design will make your product overpriced, fragile, bulky, power-hungry, and inefficient.  It will also be hard to debug, a pain to support, and you'll be at the mercy of your suppliers.  It will make you look incompetent.  

However, all is not lost.  If you implement your design on a development board, it will be straightforward to have someone (either on or off your team) customize it to remove these deficiencies.  If you lack a team, you should hire one, bring in a contractor, or have it done by a design firm.