It allows servlets to have multiple servlet mappings:
<servlet>
<servlet-name>Servlet1</servlet-name>
<servlet-path>foo.Servlet</servlet-path>
</servlet>
<servlet-mapping>
<servlet-name>Servlet1</servlet-name>
<url-pattern>/enroll</url-pattern>
</servlet-mapping>
<servlet-mapping>
<servlet-name>Servlet1</servlet-name>
<url-pattern>/pay</url-pattern>
</servlet-mapping>
<servlet-mapping>
<servlet-name>Servlet1</servlet-name>
<url-pattern>/bill</url-pattern>
</servlet-mapping>
It allows filters to be mapped on the particular servlet:
<filter-mapping>
<filter-name>Filter1</filter-name>
<servlet-name>Servlet1</servlet-name>
</filter-mapping>
Your proposal would support neither of them. Note that the web.xml is read and parsed only once during application's startup, not on every HTTP request as you seem to think.
Since Servlet 3.0, there's the @WebServlet annotation which minimizes this boilerplate:
@WebServlet("/enroll")
public class Servlet1 extends HttpServlet {