I'm not sure I follow. You mean that when you are working on something, you just shut down the application to close all your open files?
BTW, the apps need to be updated to take advantage of resuming application state, so application authors can choose to not support it if it doesn't make sense (giant Photoshop files, etc.).
I casually dabble in making music with Logic. When you open it (in Snow Leopard), it opens the last opened project.
Logic is a pretty complex application, and there are a lot of different synths and filters. The synths take a lot of memory, since they have a large number (presumably) lossless audio samples in them (think every key on a piano, times X for X number of different strike velocities).
Therefore, Logic only loads the synths that are needed for files that you have open. It actually recommends with an alert box that you close your current file before opening another one.
When you open a file, it loads all of the synths for that file - this can take a long time.
The result is, when you open Logic, if the last file that you had opened isn't the one you want to work on now, you have to wait for that file to load, then close it, then open the file you actually want and wait for that one to load.
This probably won't be a problem for Adobe users, because Adobe is really bad at making native-feeling Mac OS software, so this probably won't be supported. But for Apple's document-based media applications (Final Cut and Logic, Aperture is different because of its nature), this is a bigger issue (Final Cut has some... bigger issues right now though).
The other issue is the privacy one. I used graphic designers working for competing clients as an example, but really, it could apply to anyone that values their privacy. Personally, I like my browser being a blank slate each time I start it back up.
A final issue that I can think of is with applications that tend to be opened by files (the user clicks on a file in Finder, not on the application). QuickTime and Preview are good examples. If I open a picture in Preview by double clicking it in Finder, typically I don't also want to see the last picture I viewed as well. I quit Preview when I was done looking at that picture for a reason - I was done with it.
The APIs in Lion which enable the saving and resume are built to do their reading and writing asynchronously. So long as the developer makes use of the new system APIs, it should be a nicer experience for a case like Logic with its significantly larger files.
Try doing this with 3rd party sound libraries (e.g. East|West) and you can quickly get into loading times that are hugely longer. I love opening my projects that only use Logic's built in synths, because they load quickly compared the marathons that can ensue when I am working on a large, fully-orchestral, 70/80-track piece.
And that's before I've added other media, such as video, to the project.
I know it doesn't help much, but you can globally prevent apps from resuming. There is even a checkbox for doing so in the System Preferences, it's not a hidden preference.
I say it's not helping much since it's a global preferemce and resuming apps would be great to have – at least sometimes.
BTW, the apps need to be updated to take advantage of resuming application state, so application authors can choose to not support it if it doesn't make sense (giant Photoshop files, etc.).