Many dog shows, events and training schools ban bitches in season; some won't even allow them into the grounds where the event is taking place, let alone enter the actual competition.
Showing shows hold the dog classes all together before the bitch classes in case the dogs fall to pieces or come to blows over bitch scent left in the ring.
Active events (obedience, agility, etc.) do not allow in season bitches on the showground.
Most working bitches (police etc., guide dogs) are spayed, brood bitches kept separately.
Female racing greyhounds have their seasons chemically supressed.
Hunting hounds work in separate bitch and dog packs.
It's not just the prospect of unplanned mating, but the possibility of fights between male dogs attempting to mate, other females attacking the bitch, the risk to male dogs breaking free (or escaping) to pursue the bitch (some cannot help themselves, they lose their minds and many will blindly hunt her down); injury to or fright caused to the bitch (which may well affect her temperament from then on) and of course the risk of injury to people.
Therefore the etiquette is that in-season bitches are kept away from other dogs during their heat and shouldn't be left unattended on private land.
It's nothing to do with 'patriarchy', it's biology and common sense. Of course you don't have to walk her as usual for three weeks; it won't kill her to do fewer walks - in solitude - for a bit.
Walking her in season on a beach, however quiet - even on lead - isn't really fair, to be honest. It is a place where dogs are taken specifically to walk and swim off-lead. Many male dogs (and some females) will not react 'normally' to their handler or training in that situation.
Hormones and instinct will take over and they may detect the bitch before she is even in sight. Doesn't matter how much people bleat about 'all dogs should be under control', some won't be able to be, because their owners won't be expecting to come across a bitch in heat.
First and second seasons can be tricky anyway; the rush of hormones will have her head all over the place and her own behaviour might change: she might break away from you and go hunt out a dog for herself.
YABU