There’s really no answer except “it just worked out that way”.
In the Nineteenth Century, the presiding officers of both houses exercised real power–the Speaker in the House, and the Vice President or the President pro tempore in the Senate. (Nineteenth Century VP’s had the life expectancy of gangsta rappers, so the office was often vacant.)
The power derived from the traditional prerogatives of a presiding officer–naming committee members, controlling the schedule, managing debate, and issuing parliamentary rulings. The Speaker’s role tended to be more muscular, only because Senators were and are more independent-minded and less likely to defer to an unelected VP who might not even be from the partisan majority. But even the VP/PPT exercised some power.
In the Twentieth Century, within the Senate, leaders elected by the party caucuses emasculated the VP/PPT to the point where presiding was delegated to junior senators as a chore. All of the functions formerly performed by the VP/PPT (except for sitting in the chair and calling on senators) are performed by the Majority Leader. The VP shows up only for ceremonial occasions and to break ties.
Within the House, a parallel process has taken place, but because the Speakers were themselves leaders elected by party caucuses, they’ve been better able to resist the erosion of their power. The Majority Leader tends to fill a role more like the Whip in other bodies, and the Majority Whip . . . is more like an assistant whip. Such is the modus vivendi that has evolved over the last 100 years.