5e is dangerous over the course of an adventuring day.
I like that long rests reset everything. It's cleaner. It's a release of tension and then the next day can start fresh.
You say that the 24 hr petrification from the Cockatrice isn't a big deal, but if you wait that long you're most likely going to be failing your mission. At the very least you're probably in a dangerous area a character down.
And if time isn't a factor, what are you really doing? There is no tension there to begin with. If the party has all the time in the world to rest then it doesn't matter if they reset after a long rest or after 50 long rests.
5e is about running lower and lower on resources. That 50 dmg and 3 spell slots the party used up that battle doesn't feel like a lot now, but it will after 4 or 5 such encounters. At the players should know this. They know that things are going to get tough so they're going to feel it even early on in the day.
Players at my table do everything they can to avoid fights and to be prepared because they know that they can fail. Sometimes catastrophically with a TPK.
If failure is not allowed to happen at a table then yes, 5e is not dangerous or tension filled.