And neither was your legacy enterprise application.
If your enterprise application has been around for a number of years and a developer or vendor comes in who declares they can rewrite it in a few days/weeks/months they are probably unfamiliar with the business needs. A notion that an average installed life of an enterprise system is 5-7 years is a wrong way to approach a software engineering project -- if nothing else it is an indication of poor design and management. If the system needs to be rewritten even more frequently it is an even more pronounced sign that something is fundamentally wrong with how the organization is managing their projects.
I came across this article from ACM Ubiquity by Sanjay Kumar Pal who states:
As a testament to a vendor's ability to keep up with the needs of their customers, the percent of customers on current releases of their software should be high. The uncommonly good vendors are as high as 98%, and the percent of customers on maintenance may be as high as 99%. Furthermore, in an industry where the average life expectancy of an ERP installation is 5-7 years, inquire how many clients systems have been in use longer than 5-7 years and how many have had their systems 10 to 20 years or more. A vendor with a majority of clients over the 7 year mark is doing things right. These are unprecedented numbers in our industry and are proof of the ease of upgrading, the low need for custom programming, and the high relevance of capabilities delivered in each new release. It means you can continue to expand the system's functionality as needs arise or as new features become available.
While the article is about ERP systems the same is applicable to just about any software project out there. As evidenced by the Y2K debacle in the 1990s, software written today is likely to still be around decades from now. There are ways to evolve a software system without scrapping it.