Reduce the number of technologies, not providers of!

In some of the companies I've visited over the years, there was an internal policy that seemed strange to me: when contracting with service providers or goods providers, employees of the company should try to keep the number of providers as small as possible.
It's not the policy in itself that seems strange to me, it's the fact that it is also applied to IT goods and services.

Basically, the policy relies on the two ideas below:

1. With fewer providers, you can purchase more of the same and negotiate a better price next time.
2. With fewer providers, you can establish true relations of trust and avoid gaps between what's asked and what's provided.

That would mean that the cost per unit decrease if you remain with the same provider:
However it relies on the three following assumptions:

1. Purchasing at a specific provider will impact the price of other providers only downwards, and that will be only a small impact. This is wrong in IT, because the cost of moving to another provider is very high, because of software and hardware incompatibilities.
   
2. You can negotiate with providers. This is wrong in IT, because you're always speaking with big international companies. If they allow you to negotiate, that's within an already well-thought area.
   
3. A true relation of trust brings a really better service from the providers. This is wrong in IT, because the hardest part is always the exploitation of a product or service, not its purchase. Good relation with the provider only marginally increases quality.
   

In fact, because of incompatibilities, once you've made a move toward a provider, the cost (not price) of moving to something else shoots up. It will require time, money and will probably require you to throw away what you made in the first place.
Knowing that you can't move anymore, the provider you chose has the hands free to increase prices.
That's what happens in reality:
So, to my mind, the policy of reducing the number of providers is detrimental to IT services.

However, the real difficulty coming from the integration of very complex technologies, very differently thought, born in in very different companies or universities, and best manipulated by people outside your company (either service providers or editors), I think it is a good policy to maintain a list of technologies that you use, the (in)compatibility links between them and to think carefully before adding one to the list.