I would rephrase your question slightly: Should UX be embedded in an application team, or should it be a centralized resource? Embedding UX in the application team allows the UX professional to understand the needs of the team, and often have better access to users. Having it be a centralized resource allows the UX professionals to have better access to their UX peers, and helps engender a more consistent user experience because the UX team works together.
You've stated what is, potentially, a real business problem: a lack of consistency between your applications. Conduct research to determine whether this really is a business problem. Are you losing sales because your users can't extend their knowledge of how to use one of your applications to another one of your applications? Do users complain about the lack of consistency? Are there support issues that can be traced to the lack of consistency?
Gather data to support your assertion, and brainstorm solutions to solve that problem. Potential solutions include standards and collaboration, which might or might not mean that you have a central UX organization. Standards are going to be difficult to implement in an organization that has historically let each team do what it likes. Collaboration is often an easier sell, and might eventually get you to the standards that you think are necessary.
Personally, I've done it both ways. I was part of a centralized UX team at a large enterprise software company, although there were also individual designers sprinkled on application teams. That central UX team developed standards which were adopted by the company's flagship product, and slowly but surely adopted by other products as well. In this case, collaboration was still a challenge, especially for those individual designers embedded within teams. Creating opportunities for collaboration was a huge win in that environment. I've also been the lone UX professional embedded with the application team. I was able to be very successful in working with the team to get UX improvements into the product because I knew the application very well and was able to take part in prioritization exercises. I also had fantastic access to my users, which made user research easy to conduct. Since I was with the dev team, they often attended my user research sessions, so they were more invested in UX overall.
There is no single answer here. Determine the business problems that your UX team(s) need to address, and determine the right way to address them. Consider it user research of your own organization.