"Until some department goes for the cheapest option"
If they "find" that they bought that kind of support then the people responsible need to be fired.
Support (and the duration of that contract) is part of the purchase contract and you need to make sure you're getting what you think you're getting.
I deal with this a lot when someone undershoots my internal costings for kit with "but I can buy it from XYZ for £ABC" - my standard response is "go back and price it with 3/5 year support, next day onsite - Oh and this quote doesn't have the same amount of memory as I specified. Make sure you match it"
At this point they discover that the cheap option just doubled in price and I already have a quote from that supplier.