Leaving the console in standby is a waste of power, that costs you directly in power bills, and drives up costs for all electricity consumers as well as any effect of energy production like pollution, global warming, etc.
But the fact remains that people will choose to not turn their console off for every moment they are not using it, whether that be for 30 minutes, 2 hours, 1 day, or 2 weeks. Having standby mode is better than not having any such mode for such scenarios.
Sony (and MS AFAIK) has an ARM CPU that is auxiliary to the main AMD CPU/GPU, that is meant to handle background downloading, instant on/off (standby), and other such features which are less demanding than actual gameplay/internet browsing/movie streaming/etc.
Unfortunately, at least with the current OS/software, the ARM CPU that Sony chose seems underspecced for the job, which seems to be forcing them to NOT use the ARM chip but instead keep the main AMD CPU powered on even in 'standby' mode. This means they can't lower the energy draw drastically, as they intended to. So in the current unit, there simply isn't a dramatic power savings for entering "standby mode", it's mostly a sham. You can read articles on site like AnandTech which go into the detail for that, comparing actual power draw and so on.
Since Sony was motivated to design a standby mode in the first place, and include a discrete CPU for that task (even if it wasn't up for the task), it is almost certain that they will "fix" this feature in future units, which will most likely mean including a beefed up ARM CPU that is powerful enough to handle all "standby" functions including background downloading. Such a CPU might draw slightly more power than the originally specced ARM CPU, but drastically less than the main AMD CPU currently used... And improvements in manfacturing may even mean that a beefed up CPU on new manufacturing process may use less power than the weaker CPU on the old manufacturing process.
But whatever they do with that, current consoles with the weak/underspecced ARM CPU will not be able to rely on the ARM CPU for standby, and so they will continue to draw excessive power during "standby".