Party bags are not a tradition... Like trick or treat and baby showers and Father's day they have come across in the last 10 - 30 years. We used to have a balloon to take home, maybe. Cake was always eaten at the party.
I'm 40 and we always had a party bag at parties in the late 70s/early 80s! In fact the children's party thing was much more routine than it seems to be these days. As a small child living in the suburbs of a big city, it was pretty mandatory that every birthday from the age of 3 to about 7 you would have the house full of a class of kids, balloons, party games, party tea, candles on cake and happy birthday, more games, then home with a balloon on a string and a party bag of tat plus a squashed piece of cake in a napkin. Happy days!
The really posh might have an entertainer who did a magic show and balloon dogs, but it wasn't a party without pass the parcel, musical chairs, musical statues, pin the tail on the donkey and (a bit later) cutting the flour cake or slicing the mars bar game.
You also had to wear a party dress. Party tea inevitably included cheese, egg and meat paste sandwiches with the crusts cut off; chipstick crisps, prawn cocktail skips, hula hoops and Ringos; jammie dodgers, party rings, coconut fluff biscuits, chocolate fingers and Cadbury's Animals (the originals, not the manky horrors Cadburys sell as Animals today). There was inevitably a tray of luridly coloured jellies with squirty cream on the top, fairy cakes or butterfly cakes with hundreds-and-thousands on, and some exotic fizzy drinks (dandelion and burdock; cream soda). Plus cocktail sausages on sticks. The only item of fruit or veg to appear throughout would be pieces of tinned pineapple on sticks with cheese.
Happy birthday would be sung and the cake always disappeared to be cut up for the party bags (by that point each child had normally eaten his or her body weight in party rings and jammie dodgers anyway).
The bags always had some kind of e-numbered chewy sweets and lollipops plus a range of delightful plastic tat (plastic snakes, ball catchers, flipping frogs, whistles and bouncy balls).
The most coveted item in any party bag would be one of those necklaces or bracelets made out of sweets. Happy days!
You were no-one without a party exactly like this when I was a very small child! The only reason why people don't seem to do these parties these days where I live is that most people's houses are too small.... no big 1970s boomer pads for most families these days.