Just a curiousity question, so don't get me wrong for I very much admire and have high respect towards the entire Mercury project, Alan Shepard (the first American in space, a national hero) and Gus Grissom (the 2nd and last Redstone astronaut) and I'd fly on a Redstone into space myself if I could. My question only deals with the point of building and testing the Redstone rocket during the space race while having the X-15 spaceplane.
Since both the Redstone and the X-15 were suborbital spaceflight vehicles I wonder why did they bother with the crewed Redstone rocket in the first place instead of focusing on bringing a man into space on the X-15 while the Mercury project could have put more effort into the crewed Atlas rocket. The X-15's first powered flight was on 17 Sept 1959, flown by Scott Crossfield. So from there on, about two years before Vostok 1 and Mercury-Redstone 3, the USA were theoretically able to fly a man into outer space. However, the X-15's first (U.S.-recognized) spaceflight was as late as 17 July 1962 (Robert White) and its first FAI-recognized spaceflight on 19 July 1963 (Joseph Walker). On 30 March 1961, a few days before Gagarin's flight, Walker reached an altitude of 169,600 ft becoming the first man to reach the mesosphere. If Walker would have flown 19 miles higher he would have become the first man in outer space according to the U.S. definition or 31 miles higher and it would also be an FAI-recognized spaceflight.
Why wasn't Walker allowed to go higher in the intensifying space race? Why were there so many X-15 flights going comparably low instead of putting more effort into reaching outer space? I don't think building and testing the crewed Redstone rocket was a waste of time, but from the space race's point of view (and perhaps also from the taxpayer's point of view) it might have been one. If more effort would have been put into X-15 spaceflights, the first man in space could have been an American, and also perhaps the Mercury spacecraft would fly sooner into orbit, if more effort into the Atlas rocket would have been put.
Therefore, my question is: Why wasn't put more effort into flying a man into space by the X-15 and built the crewed Redstone rocket instead? Were they concurring programs (like today's Crew Dragon vs CST-100 Starliner)? I don't think so because as said there were many comparably low flights of the X-15. The only advantage of the Redstone rocket I think of is that since apogees around 115 mi (185 km) were reached, noone doubts that Shepard and Grissom flew into outer space, becoming astronauts, while the X-15 spaceflights may be somewhat controversial (even the FAI-recognized ones) and the Soviet Union could have claimed these wouldn't be spaceflights by establishing an own threshold. But that's a bit far-fetched I think.
Note: If the flight Mercury-Redstone BD didn't occur but Alan Shepard was launched instead, he would have become the first man in space. But that's a different story, NASA was just overprotective.