Does it really cost that much to maintain servers? Not a good look for Sony
Not much.
And they may be leaps and bounds worse than Microsoft in this regard which also isn't really defendable other than the fact that they are much smaller. But support for things in industries dries up all the time as they age. Video games aren't really special in this regard.
I think your HBO example isn't a particular good one, because these streaming services pay a big fee to license the content or have to create them new. Your example is more equivalent to PS Now or Gamepass losing games or games getting delisted from the various online stores imo.
Putting up servers obviously cost money, but Sony earns a ton of money and other companies without PS+ money can keep servers alive. Blizzard for instance.
Then there is Microsoft, which has build a much better online service in Xbox Live, because their matchmaking servers take care of all the games and the backend uses VM. That's typical today and the scalability is awesome.
For example if someone doesn't play Shadowrun then it simply doesn't take up any resources on Azure. When people want to play a game, the services automatically scales up.
That's the reason they don't need to shut down servers and in 99% of the time they don't. I am not really frustrated by Killzone, but I think there are two valid demands as a consumer.
1. Announce the server shutdown or downtimes when they happen or beforehand.
2. For the love of gaming get PSN with the billions of PS+ money up to modern standards you see in different industries and then Sony wouldn't need to shut down servers.