Why is anything packaged in a carton? In order to take advantage of storage and/or transportation costs. Cartons are totally symmetrical and can be stacked. Toothpaste used to be a solid, and was purchased in a square (or round) tin. But that was back in the 1940s, and some things have improved since then.

it is packaged in case during transportation the lid opens or the packaging breaks so the toothpaste wouldn't get on anything. As well, in the carton, no one can squish the toothpaste

to prevent customers from opening and squeezing the tubes. There is one toothpast that is packaged in air squeeze metal can, but it think it is for Dentures. and it is packaged so it can't be squirted.

For ease of handling & shelving, to prevent damage to the tube, to provide space for ingredients and advertising.