The low energy density of batteries does matter for applications at scale. Because you need buildings to put the batteries into, which will need space, and have to support the weight. You will need an awful lot of space for battery storage in the megawatt, let alone the gigawatt range.

For uninterrupted power supply in many applications, you can even live with the low energy density of lead acid batteries, because they typically only have to bridge the short time time until the emergency generators (usually diesels, in some applications, gas turbines) have started and spun up to their operating speed. This is, depending on the size of the generators, a matter of seconds (small generators with truck size engines) to minutes (large generators powered by ship engines). In energy intensive industrial processes with backup power, usually only the control systems are on battery based UPS, while the actual processes will lose power for a short moment until the generators kick in.