Why do we need to fold the border of filters? Standard and V60 paper filters require we fold the border before spreading them for dripping.

I believe this is just because of their manufacturing process. But would there be any other reason?

Folding that border makes the surface uneven in the end, and it can sometimes be harder to control the water flow.
I did a little bit of research at the site of inventor of the coffee filter. It's Melitta from Germany. In the german FAQ I found the following:

Warum falte ich Filterpapier vor dem Einlegen um?
Damit die Kaffeezubereitung optimal funktioniert, muss das
Filterpapier genau in die Form des Filters gebracht werden. Dies
geschieht, indem Sie die beiden geprägten Ränder umfalten. Das
Filterpapier schmiegt sich dadurch an den Rand des Filters an und
sitzt tief im Filtereinsatz. Durch diese gute Passform kann sich das
Filterpapier während des Brühvorgangs nicht einklappen

In English:

Why I fold the coffee filter?
For a good result the coffee filter must be in exactly the form of the
drippter. This is done by folding over the two embossed edges. The
coffee filter is nestled by the edge of the dripper and sits deep in
it. Through these good fit, the coffee filter can not collapse during
the brewing process.

Additional fact: The coffee filter was not invented by Melitta the company, but by Melitta Bentz.

Sorry for that bad translation. My English is really not the best. Please improve me!