Well you're kind of missing the point. Let's say I'm a developer who wants to do a travel website. I shell out my money and I do a bang up job. My site's pretty popular, everyone's happy.
Later the BBC want to do a travel site, do they shell out their money to compete with me? No, they dip into the huge pot of money, (~2 billion GBP?), that's available to them 'cos the government force us to pay a licence fee. That's the point.
No one's saying the BBC shouldn't do these sites, they're saying if they want to use licence payer's money then they have to do "public service" sites and if they want to do commercial sites and compete with commercial companies then it has to be on an even
footing, i.e. they have to use their own money. That seems fair to me.
Your Google / Yahoo analogy would only hold up if Google were receiving billions of dollars from the US government to help develop their product and Yahoo were having to survive on what it could earn commercially.