Actually, many 16-bit programs were made to work with Windows XP and not just DOS.  For example, I had a Canon scanner that simply wouldn't work with 64-bit OSes because it used a 16-bit driver.  Similarly, I have a 32-bit program with 16-bit components which allows me to transfer music to a hard drive which is installed in my car.  That program was meant to work on Windows XP and unfortunately the developer of the program has now essentially ceased support, so again, when I switched to my 64-bit version of Windows Vista 2 years ago, the program became largely unusable.  Now then, in some cases, others have managed work arounds by changing some of the requirements for some of the files (for example, for the latter program, I was able edit the .msi file from the partially extracted original program.  This allowed me to remove the OS requirements which allows the program to become usable again).  But this isn't something that just anyone can do, and not programs will work that way.

But as I stated, 32 and 64-bit programs have become much more commonplace, so it's no longer the same issue it used to be.  Those who require the legacy software should probably just keep their old computer for that specific purpose for when they need it, but otherwise, they can move on.