Is the counter argument that CBeebies is what makes it difficult for the commercial sector to compete. Of course though we know from the history of absolutely everything withdrawing a public service under the belief private companies will step in to fill the gap never comes to fruitition.
Given how parents of very young children use CBeebies and other channels, I'm not sure that there is a commercial opportunity that ca be exploited by the private sector here. In other words, parents actually rarely watch the adverts and the pester power of 6 year olds and younger is not quite as developed as the audience for CBBC.
I'm certainly not an industry expert but I think CBeebie's programming budget (before other costs) is £28m a year. In order to have a chance of breaking even at these figures, they'd need to sell about £3,200 an hour on average of adverts to break even just the programming budget.
Given the limited number of companies which do advertise on other channels targeting the same audience, I am not sure that there are enough advertisers with deep enough pockets to make a profit-driven CBeebies competitor viable.