Advertisers pay a great deal of money for their ads to appear somewhere between the start and the finish of a sporting event. Football has a convenient 20 minute break in the middle, where plenty of adverts can be shown.
Until Bernie Ecclestone introduces a tea break into the middle of an F1 race, you'll have to put up with ads during the race.
The other important factor is that many people are only interested in the actual sport, not the chit chat after. With Forumla 1 after the race has finished many people would switch over rather than hang around waiting to see what happens after (i.e. not a lot). With football at half time people will still be tuned in waiting for the second half.
One thing I'm sure we will see in the future is small advert bars which pop up on the bottom of the screen during a game.