At the minimum QoS has to be involved at the LAN switch level for VoIP because as mentioned it does not deal well with waiting for browser data. In fact it is arguably more important than overall bandwidth as it isn't a high bandwidth user compared to browser data but it certainly requires stable throughput and low latency. In a hosted VoIP environment (converged voice and data) QoS from the CPE to the carrier are equally as important.
A 1 second delay in loading a page is inconvenient - inserting random additional delays as low as 50-150ms in RTP causes static, pops and delays which make conversations difficult for many people. You would be surprised how sensitive some people are to subtle differences between VoIP and PSTN calls - volume being one that most people struggle with.
Soft phones are the easiest example of this since they share CPU and NIC with the rest of the OS and the browser. When the CPU or NIC become bogged down the RTP suffers drops and delay. I am sure Skype users can relate.
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