Apparently I didn't fully understand the licensing of MSDE, since Microsoft advises us on how to...

Build dynamic, data-driven Web applications with Microsoft ASP.NET and MSDE 2000 using the Workload Governor to limit the number of concurrent operations that the database engine can perform.

[ Using MSDE 2000 in a Web Application (MSDE 2000 Web Resource Kit) ]

This continues with SQL Server 2005 Express, but the connection pool limit seems to have been increased to 25 simultaneous connections.