I used to carry paper handkerchiefs all the time, ( hayfever) in my pants pockets, and could hardly get them out, the pants were not toight, but normal, and as we know front pockets are sometimes very difficult to access. Skirts may have some more leeway, as they do not follow the thighs as do pants. I wear mostly skirts without pockets, and that in itself feels very comfortable, not having any things propped into the pockets, unpleasantly tight against me.
So We generally have a mobile, which you can better not sit on all the time, ( also very uncomfortable, ) some form of wallet for all soorts of credit cards, drivers licence, motor vehicle registration, passport or Identification pass etc, a handkerchief or paper examples, a comb, house key, most likely a bunch of keys, house, bycicle, shed / garage, car / motorcycle etc. And any number of other handy junk. a role of peppermint, Not even mentioning for smokers

their needs.
And when men do wear panty hose, a pair of reserve panty hose, with cotton gloves, a pair of sunglasses, in a glasses box, and maybe something else. I wear my prescription glasses, and have my prescription sun glasses with me.
My mobile hardly ever gets used, but it is handy to have it with you. Why otherwise have a mobile?
So with all that stuff, whether it be a "man's" bag or anything else you like, a bag is darned handy.
I have all mu stuff in a handy bag with several small compartments, and take it with me everywhere. As always, be ware of thieves.
I have never had anything im my pants other than a comb and my handkerchiefs. Keys would wear out the pockets fast, and fel very unpleasant. Small change purses idem dito. Wallets, they get stolen very ese asily from rear pockets and we here in the Netherlands had up to now large papers for driving licences, which had better not be folded. So I usually had my papers in a wallet inside my jacket.
I am so happy with the bag, and I got used to it very fast. But Never forget it..I mean leave it behind in a store or someplace...

It'l be gone before you can say.....
But it's not the fault of the bag, it's us having to have all that stuff with us.
So yes I carry my bag everywhere.
In the past I used to have a army issue canvas bag, but that had gotten worn out. Had my lunch in that too.
A man is the same man in a pair of pants or a skirt. It is only the way people look at him that makes the difference.