It has to do with the game’s open world nature.
One of the best, and most under-appreciated, innovations this generation is the ability to play a game even as it is installing- when you download or install a game on your PS4 and Xbox One, you can start playing it even before it has fully installed, as long as a certain minimum threshold of important game data has been copied to your hard drive.
Fallout 4, on the other hand, does not work this way. Fallout 4 has you go through the full installation of the game first before you can play it. Digital Foundry speculates that this might be because of Fallout 4’s absolutely open nature.
“We can only really speculate as to why Bethesda chose to bypass the consoles’ ‘fast start’ mechanism for playing Fallout 4 while the game continues to install behind the scenes, but it’s likely down to the fact that the initial, very linear introduction sequence is over fairly quickly,” said Digital Foundry chief Richard Leadbetter. “After that, you have immediate access to the open world – and the game cannot anticipate the direction you’re likely to travel in.
“Rather than impede progress with obtrusive installation screens and progress bars, it seems that the developer has chosen to ensure that all the data is installed onto the hard drive ahead of time – just like a standard PC game. It takes longer to get into the game as a consequence – and you’ll need to preload the entire game if you’ve bought the digital copy – but I’d say it’s the best solution overall, even if it’s not completely ideal.”
So… yeah. A sandbox like game like Fallout 4 comes at a price, I suppose.