See, this is where people who don't have experience of it are making wrong assumptions.
If you only have experience of bfing a small baby, or, say, up to about a year old, you'll think of it as something babies do and do regularly.
But when you have an older child who still bfs, you can start to set boundaries. So, you might say, "Only at nap/sleep time" or "Only on the sofa at home" or "Only first thing in the morning/before bedtime" and, as your child gets older, they begin to understand when they can bf and when they can't, etc.
As for precluding other people from involvement with your child - no, it really doesn't. Plenty of women breastfeed older children and work/go away/go out, leave their children with other people, etc. Lots more don't, of course - but it's perfectly possible. Children who are breastfed soon learn that mum has the milk and other people have different ways of comforting them/getting them to sleep, etc.
And, in fact, if you bf an older child, it becomes part of the range of things you do to comfort/soothe your child. It is a very handy thing to be able to put your baby up your top when they are too tired to settle, etc - and it is also very handy to be able to snuggle down next to your older child and bf them back to sleep - but it's not the only thing you can do, by a long way. Children who are bf still have cuddles, suck their thumbs, still have favourite toys/comforters, after all.