Except the amount of money to buy 25 minutes of advertisement for 11 DAYS will be more expensive that strait advertisement.
Broadcasting means even if it flops they are still being payed by episode, the loss in incurred by the network that still gets sponsor and advertisement to lessen the blunt.
Also DVD sales in Japan are shit, a series might sell 250,000 that makes OVAs not being ver attractive since there is no recover from a flop.
If studios would be paying for airing then Anime would be dead, few series makes it on the DVD market and most series are adaptations ... we would be reduced to Sunrise if that was true (and Sunrise would be doing nothing but shitting Gundam since Gundam is nothing but Gunpla advertisements for Bandai).
You might say the studios broadcast pay for the series is usually not enough to cover animation and operation costs incurred for the series, that we know (NGE is a example of that) but that is a different issue, also that studios usually "re-animate" for the DVD releases but still its not going to cost as much as doing it from scratch (voice acting is already done for example).