Agreed!!!!! From a common sense point, you would/should lose carbonation because the tank will equalize. I say common sense because I am not applying any actual scientific formulas. The drop in carbonation is not as drastic as the beer instantly dropping to the pressure that you now have the regulator set at. In my mind, you have pressure coming in from the CO2 AND you have CO2 coming out of the beer. This should actually increase the pressure inside the keg above the serving pressure. You can see this when you take fill a glass from a keg after not having done so for several days. The first glass usually has lots of head. The beers after it (if drawn within the next couple hours) are normal. The pressure of the beer releasing the CO2 and raising the keg pressure (above the serving pressure) will get less over time until the beer eventually is low enough in the keg that it has been able to release enough CO2 and is now carbonated at the pressure you are serving at. I have been kegging since my second batch and have never had an issue with severely reduced carbonation at the end of the keg. However, there is nothing saying you can't blast a half full keg at 30 PSI (here the number comes again) for a day to put some additional carbonation back into the beer. I have done this as well.
In regards to the second part. Setting the beer at 30 PSI for just a day then dropping it will NOT carbonate it enough. I have forced carbed beers (30 PSI and rolled the beer back and forth for 90 seconds) and still not always had the beer sufficiently carbonated. The OP was asking for the traditional way to carbonate without force carbing. All setting the beer at 30 PSI for a day will do is take a day a two off of the week plus of time it takes for the slow carbonating method. Now you could set it at 30 PSI and just leave it until the beer hits the desired carbonation level. I have done this too. However, this could still cause over carbonation (I am not worried about this mind you) and the OP was asking for the non-forced carb way.
I hope this clarification makes sense.