Short answer: Cost in time and money to build and retest a standard operating environment does not generally make it viable.
Many updated browsers require up to date hardware and operating systems. This is a massive cost in many organisations, who spend considerable time and cost building their standard operating environment (SOE). Depending on the duration of hardware leases, this is done every few years, when they evaluate what existing systems they have for their internal processes and what is the minimal risk to business continuity. "Cutting edge" = risk. The impact on production systems unexpectedly failing due to an upgrade can cause huge financial and perception repercussions.
A number of years ago I was working in a large financial institution when they were doing a roll out of a new SOE. I was involved in the testing of a number of legacy systems with the new environment and their sociability with existing and new systems. This whole process took several months. As you correctly state, many internal systems run on browsers. Unless there is a business need to upgrade these systems, it will not happen.
So sure, it would be great if organisations could simply upgrade their hardware, software and browsers to the latest version(s), but due to the large cost and risk, it normally doesn't happen unless absolutely necessary.