In English, one might say "the women visit" meaning that they sit together and chat. They might do so at a restaurant. Can מבקרות be used this way? If so, then would this be a valid translation: "The women visit at the new restaurant"? With the "at" the women are there to see each other; without the "at" the women are there to try out the restaurant.
Almost: another meaning of לבקר is "to criticize" - לבקר את המסעדה = "to criticize the restaurant" (note the different preposition in Hebrew compared to "visit"). The profession "critic" is מבקר, and a "critique" is ביקורת. So, theoretically, לבקר את המסעדה = "to write a review on the restaurant", but I think it's not really used like that; instead we'd say לכתוב ביקורת על המסעדה.
There are verbs which are used ONLY with ב, מבקר is ine of them, מטפל ב, is another one of them (to handle something, to take care of something, to take care of someone), it is hard to explain why this is. The teachers in Ulpan recomend tonlearn each verb with its corresponding ב, ל, מ,את etc. And if you do that for for the first time of the Hebrew journey, without asking yourself too many time Why this is... By the time yoy will know enough of them, it will become to you obvious why. But for sure there is an explanation, which is very logical. You would have to know grammar terms which are not taught in the western schools and only taught in Russian schools or in linguistic western colleges.
I'm actually quite sure there is no deep reason why each verb goes with which preposition. Like most things in language evolution, it's about analogies to familiar constructs: when a new verb starts being used, speakers draw analogies from other verbs they are used to and which seem to them similar in some ways. Also an already-established pattern for one verb might change because speakers start saying it differently, drawing analogy from other verbs that they deem similar.
I'm heavily influenced in this thinking by Guy Deutscher's amazing book, "The Unfolding of Language".