Centralized systems like Mathjobs are really the exception rather than the rule. In most other fields of academia, and in practically all industries outside academia, the norm is that applicants for a job will apply through the employer's own HR system. And university HR policies are usually written to assume that as the default procedures. They may need to comply with laws or institutional policies on confidentiality, record keeping, non-discrimination, etc, which are harder to ensure with an outside system.
So, if a department does want to use a centralized site like MathJobs, then usually someone from that department has to lobby the university HR office to get an exception from the general policy. This may or may not be successful, depending on the flexibility and/or risk aversion of the HR and legal people, and/or on how much internal political capital the department is willing to spend.
Sometimes there is a compromise, where the bulk of the application material is collected through MathJobs, but the applicant also has to submit at least a pro forma application through the university's HR system (maybe entering only their basic personal info and a generic CV).
Another argument that's sometimes raised is that MathJobs is something of a victim of its own success: it's so easy for applicants to apply that they very often apply to basically every job they see, even those for which they are not at all qualified, or do not fit the expectations. (E.g. fresh PhDs applying for full professorships, algebraic geometers applying for math education faculty positions, etc). As a result, employers using such platforms can receive a huge number of applications, often in the hundreds. Even if they have very efficient procedures to screen out those applicants, it takes time, and if they do not have such procedures it is going to take a huge amount of time. (For instance, in my department, every application that meets the minimum requirements - which is usually just a PhD in the desired field - must be read in its entirety and scored on a formal rubric.)
As a result, some people think that the extra time burden of requiring applicants to apply through the university's own HR system is actually an advantage, as it forces applicants to "show that they are really interested". Personally, I don't agree: I think it just tends to skew the applicant pool towards people with a lot of free time on their hands, and that it's disrespectful to candidates to make them waste their time filling out forms in order to prove their interest in the position. I would rather see an employer keep using MathJobs, and if they really need to make candidates prove their interest, add a requirement for a special essay about something that's actually directly relevant to the position.
Cost is also a factor: MathJobs currently charges an employer about US$500 for one job posting (or about $800 for multiple postings). It may not be that much in the big scheme of things, but it means that a department lobbying to use MathJobs has to also lobby for the administration to pay for it, or come up with funds from their own budget. At my institution, the normal advertising budget for a faculty search is $500, so if we want to use MathJobs, then we can't advertise anywhere else unless we get special approval for extra funding.
You're right that an internal system has a cost too, but usually it's some off-the-shelf software-as-a-service package that the university has already licensed, and so the marginal cost of posting one more job is basically zero.
