The number of professions don't go up, and will certainly diminish in the future. Switching professions as a young person without a dependent family is not all that hard. But as a family father/mother, it's not always possible to spend the time to switch professions. Today most of the jobs have qualification, experience and age requirements.
> There is certainly temporary pain endured by workers who are displaced by the innovation. But it is folly to subsidize work that is no longer in demand.
That should not mean the transition could not be smoothened, though.
Let me comment on your example. In todays economy things are sold, not shared. So I need to have something to give in return for the fish that the fisherman (the guy with the fishing rod) gives me. I can dive for scallops. But another guy comes with a scallop-collecting machine and the fisherman does not need my scallops anymore, as he can buy from him cheaper. So I start guarding their stocks for them in return for fish and scallops to eat. But then they invent an automated system for defence of their stock, so my labour is unnecessary now. I need to eat, so I start farming, and as I can't live on herbs merely, I trade some of my crop for fish and scallops. But one day they start importing it from another island for cheaper, and stop buying from me. I can't support my farm year-round just on my crops, so I switch to herding a flock of sheep, and trade meat for fish, scallops, and herbs. But someone comes and builds a modern meat production plant, and I can't sell cheaper than him, so I'm out of business. Given I can't live on my herds' meat only, I need to move on. And while the island slowly thrives with newcomers as the services are increasing and life is becoming easier, the amount of my opportunities diminish. Finally I start up a little market where I sell stuff that I import and/or buy from local providers in order to earn the money to buy fish, scallops, herbs, meat and other stuff. But comes a big coop and drives me out of business. I resort to taxi driving in order to survive, but apps and ridesharing replace my business. I go around seeking a job, in factories, coops, fishmongers, etc., and I find a job as a cashier in the local coop. But an automatic cash largely diminishes necessity of a cashier, so, I'm moved to the big depot of the coop. There, automation, growingly replaces the need for human labor, and as I'm rather inexperienced, I'm laid off. Because they don't want me to become a hobo and pose 'em a threat, some institution gives me 'unemployment money', so that I can survive. I don't want to survive, I want to live, but I lost the chance to become a white-collar while I was trying to catch on, I didn't have the time to focus on one thing and become a professional. So I sort of live as a dependent of the social welfare system, barely surviving, without human dignity. Furthermore, I'm excluded from some parts of community by social code, and am informally a second-class citizen, as I live off the taxes of others. A family is merely a dream for me, as I don't have the money to support it. And should I already have a family, my kids and my partner are at least frustrated at me as I'm a dysfunctional member of the family, though it's also possible that I'm excluded.
Here, a more realistic allegory.