A one-year-old has no idea it is their birthday. The party is not for them, and planning it as though it is leads to a lot of wasted effort.
It is for the adults who made it through the first year, and for the photographs. Both are real reasons to have a party. Neither requires the baby to enjoy a single moment of it, which takes the pressure off entirely.
A one-year-old's schedule does not move for a party. Put the party inside their existing nap and mealtime pattern, not the other way round, and the day goes far better for everyone in the room, baby included.
The rest of the party is really for the guests — food, chat, photos. Do not build activities "for the baby"; a one-year-old needs a safe floor and their own toys, not a programme.
That is a judgement only you can make about your own priorities and budget — plenty of families skip it, and plenty love doing it. Neither is wrong.
Only if you want to see the parents. The babies themselves will not play together yet; they will mostly ignore each other in the same room.
Part of our guide to Filling the unstructured days.