One of the crucial factors in getting SpaceX going and becoming profitable was and is the funding from that budget you're talking about. NASA and SpaceX are not

One of the crucial factors in getting SpaceX going and becoming profitable was and is the funding from that budget you're talking about. NASA and SpaceX are not in competition, they have different goals; getting the private industry to produce cheaper rockets so that NASA can spend more on the actual space exploration (69 ongoing missions!) is one they are achieving with these bets on SpaceX.