Think of the medals as a 10,000 points for 1st, 100 points for second, 1 point for third.
With less points positions, the championship will almost certainly have several contenders still alive for the championship win at the last race, so it should be more exciting in an "anyone can win it" sort of way. But it certainly removes any reward for being consistent, unless you're consistently winning.
What I'm most afraid of is seeing lots of 2nd place or 4th place drivers doing really dumb shit on the last lap to the 1st or 3rd place cars, taking them both out of the race.