If the packets stay within your own network then you can apply and control QoS polices using these DiffServ markings - effectively giving some traffic higher priority than others, with sensible limits and safeguards.
Once you go into someone else's network or onto the internet, most networks will reset or remove any Diffserver marking at the ingress point to the network.
This is because the network provider itself typically wants to decide which traffic, if any, to prioritise and will not be happy to leave it to clients of the network (unless you have an SLA or other agreement with the network provider to support some QoS scheme - some providers will support services which offer higher service then the typical best effort level, for example BT in the UK offer a priority broadband service, although I am not sure how much take up there is on these types of services).
Note that the service providers will often have QoS set up right to a customers home or premises to provide services like VoIP, IPTV etc - these require better than best effort generally.