This question was discussed intensively back in the late ’90s in Switzerland and it was finally resolved in 1999 when MySwitzerland.com the site for the Swiss NTO was built with a fully functioning hotel booking engine with the widest coverage of accommodation across the country, something no other organization was offering. Of course, there was opposition by entrenched interests including travel agents.
The basic question here is not one of competing with private industry but to fulfill the mandate which in most cases is focused on increasing visitor numbers and expenditures and not on protecting existing distribution channels, both domestic and international. While a DMO booking engine by itself is today not a huge profit center, it is an essential customer service tool of increasing importance.
With the travel planning process increasingly starting on destination websites it is only consistent with a customer centric philosophy to offer those interested and motivated potential visitors an immediate possibility to purchase their vacation right then and there. Handing them off to all sorts of third parties is a pre-internet business model.
At the very least a DMO website should be a booking platform for supplier and third party travel offers. Experience has shown that a majority of these partners appreciates additional distribution opportunities for their products. Channel conflict management is an issue addressed by many other industries and has to be tackled by the travel industry too. Again, what should get top priority in the discussion is customer focus and not destination internal politics.