1.) Most modern smartphones allow you to disable the cellular radio, using something commonly referred to as 'air plane mode.' Thus, you are left with a standard PDA.
2.) You can also remove the SIM card from GSM models, which effectively does the same thing as above, but prevents kids from simply 'turning it on.' Again, you are left with a standard PDA.
3.) PIM software on smartphones is stored locally, with cloud storage being an option. Thus, you can synchronize the data with your computer or not synchronize at all, either way avoiding uploading personal data onto the internet.
4.) Batteries and battery management technologies have evolved quite a bit over the years. For instance, I typically got just under 4 hours of use (combination of video, audio, and productivity) on my WindowsMobile 2003SE Dell Axim X30 whereas the current WindowsMobile 6.5 HTC HD2 gets a solid 10 hours, and that's with the 3G radio enabled.
I too would like to see PDAs remain an option for consumers, but falling smartphone prices and the ability to use them as PDAs only make PDAs a dying breed.