University's motivation for having tenure-track positions Suppose I used to hold a tenure-track math position at a R1 institution, but then I was denied tenure. Assume I do not care about job security (and never cared) and I would be more than happy to keep working under the same conditions and would work just as hard as I worked before tenure denial. The question is: what are the reasons why the department would not be happy to keep me (under the same conditions)? 

Some hypotheses:


Me working at the department is beneficial for the department at any given point of time. If this is true, then they should be OK with me remaining in my present position. 
Accepting someone for tenure-track is a calculated risk the department takes (because it can not judge purely from the post-doc record whether one is going to be a great researcher or not). Now that my tenure-track is over, they have figured out that I am not good enough and it is beneficial for them to kick me out. 
For an average person, the possibility of tenure is a strong motivator. It is beneficial for the department to have someone who has been promised tenure at any given point of time but it is not beneficial once the person knows they won't be given tenure. I am just a weirdo who happens not to care.
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.