The answer to this question is subjective based on your play style and "ability" to play the game. Daemon fights are built to be more difficult than daytime fights. A person's knowledge of the combat system and how to use their equipment becomes increasingly more important as the game goes on. However I can answer some direct points.
Will nighttime always be dangerous?
Yes, nighttime will always be a decently dangerous undertaking. It will always be more dangerous than day time. During the main story, the daemons become both stronger and greater in numbers. As your level up, and more importantly, spend your Ability Points, your party becomes drastically better at being able to handle the daemons however, so it becomes less of a problem than at the beginning of the game, by quite a large amount.
UPDATE: NO It appears the demons at night stay around the same level throughout the game. (Exception being the endgame chapter where its always night.) Even while in chapter 15 and im level 99, the demons still seem to be mostly around the mid 30's. There may be some unique exceptions, but I havent run into any.
Also, as is mentioned in the comments, you can unlock a set of headlights for the Regalia that lets you drive at night without running into any daemons.
Will the nighttime daemons continue to scale up in levels so that they're always stronger than me? Or will I eventually be on equal ground with them?
No, the daemons will not always be higher level than you. They tend to be higher level than the beasts during the day based on the chapter your on, but if you complete enough sidequests you can out level the daemons.
In Final Fantasy XV, the creature crossing are an aesthetic that means to breathe a degree of life into the world. As you noted Prompto posits where they may be headed and Gladio suggests following to find out.
Should you find the desire to satiate piqued curiosity, you'll find they simply cross the street and run into a nearby field where you can mercilessly slaughter and them for their horns just as you would had they not crossed the street and made you wait 30 more seconds before driving along the otherwise uneventful countryside.
So no... it doesn't "do" anything.
Best Answer
Resting at a campsite offers a few more mechanics that resting at a inn or trailer.
Buffs: The major reason is the buffs you can obtain from foods that Ignis can cook. You do not obtains buffs at an inn at the cost of bonus XP
Tours: It is not important to rest at every campsite, but there are a few camps that provide special side-quests known as Tours. These tours are a set locations, and offer different rewards and character building
Training: This provides different combat options with your allies to obtain some AP and different rewards.
As a side note, if you wish to wait to cash in your experience at an inn to obtain bonus XP, you can always equip the Nixperience Band from the Holiday Pack DLC (which I believe is automatically included in the PC version)