I don't see why. If the Steam-DRM'd version of a game requires Steam installed in order to play, they can just add the Steam package as a dependency.
Possibly a bigger issue would be that Steam has incremental updates (fixing a bug in a game requires downloading a fixed binary but not the multi-gigabyte data files) while most Linux package managers do not support incremental updates (when Debian releases a new LibreOffice package that fixes some dependencies for the s360 archictecture, I still have to download hundreds of megabytes of changes on amd64).
There is also the issue that a Steam game may have dependencies on different versions of certain libraries than those which may be shipped with popular distros. You also have to think about people with custom PPAs etc.
I think it makes sense for Steam to be isolated from the rest of the system as much as possible.
It is also helpful to Valve if it is as consistent with Steam on other platforms as possible.
Game downloads can be pretty big and take a while too, I'd rather not have apt locked for an hour while it grabs some large game update.
In Linux game packaging, this issue is often resolved by having a separate package for game data. This is also a neat workaround for licensing differences. For example Quake 3 is now open source, but the game data is still under commercial license. Distributions now offer just the game binaries built from the source and you have to buy the data yourself.
Possibly a bigger issue would be that Steam has incremental updates (fixing a bug in a game requires downloading a fixed binary but not the multi-gigabyte data files) while most Linux package managers do not support incremental updates (when Debian releases a new LibreOffice package that fixes some dependencies for the s360 archictecture, I still have to download hundreds of megabytes of changes on amd64).