University's motivation for having tenure-track positions
In most jobs in industry, new employees go through a probationary period during which they can be let go (fired) for poor performance without the protections and benefits that more experienced employees might get.  If a new employee isn't working out, then they'll be let go during this probationary period. 

In higher education in the US, the (customarily at most 7 years long) tenure track is an extremely long probationary period tied with policies that (in the name of academic freedom) give tenured faculty very strong protection against being fired or laid off. 

When a tenure-track professor is denied tenure, the university has decided that they're not doing well enough in the job to justify a lifetime commitment from the institution.  There are significant costs associated with recruiting a replacement, as well as significant consequences for the morale of other junior faculty,  so these decisions aren't made lightly.

Allowing a tenure track faculty member to continue as non-tenured faculty member after you've denied them tenure has problems.  In addition to lowering the morale of other tenured and tenure-track faculty, it runs afoul of the guidelines for tenure promulgated by the American Association of Union Professors (AAUP) that say that tenure must be granted after seven years of service.  

It should be noted that the tenure system is in a significant decline in the US.  More and more, teaching and research work is being done by people in non-tenure-track positions and the number of tenured faculty is declining.