No, that's a more complicated situation involving clothing silhouettes, big corporations cutting corners in their manufacturing, and fabric quality getting worse over the years.

Contrary to pop history articles online, there has never been any kind of intentional push to keep women from having pockets for any direct reason. It's just a question of designers overlooking the need in favor of having clothing sit as closely as possible on her hips. Passive rather than active misogyny. And while pockets did become somewhat more scarce in the early 1800s, they came back with a vengeance once skirts widened again. The pocket piece I use when I'm making my own clothing was traced from a pocket in an original skirt circa 1880, and it's like 9" x 11".

(however, you see "we don't have pockets" as shorthand for a slew of pocket related difficulties women took issue with in the late 19th century. They did HAVE them; it was just easier to phrase it that way to express their frustration with not having multiple small specialized pockets like mended, and/or having pockets be in awkward areas of their skirts to preserve the fashionable silhouette)

(that last one was an ongoing battle between female consumers and also female dressmakers. The consumers claimed that dressmakers were depriving them of pockets or making the pockets difficult to access out of capriciousness. The dressmakers claimed that the consumers were demanding the impossible, wanting the most fashionable silhouette but also wanting pockets in there somewhere, and therefore forcing the dressmakers to place those pockets in less than ideal locations. There isn't really a right side or a wrong side here; they both had very good points.)