Kids NEVER allowed an outsized marble anywhere near 1" in a game of marbles. Almost all kids played with 5/8", which is why they are the most common size. Older kids might play with < 3/4", but at the older age they generally moved on from marble playing. Also keep in mind that 3/4 - 1" dia. was too large for most kids to shoot properly due to the size of their hand. A larger marble has a real advantage over players with smaller marbles.
At the marble tournaments I have been to, all kids played with 5/8". Also, IIRC, true agates were not allowed in games using glass marbles.