This is potentially illegal. Look up "tortious interference".
> or maybe you want to keep the relationship going to leave the door open for future employment opportunities
In my experience, my boss is usually pissed about me leaving anyway, even with 2-week notice. And then they try to backfill my position ASAP anyway.
> the industry is small and many people bump into one another more than once in their careers.
I switched into tech from a very small industry. Tech is huge in contrast to a lot of other industries. And people bumping into each other has a smaller affect than interviewing for better job.
I am not here to convince you to give notice, but only stating the reasons people do give a courtesy notice. As always there are people who don’t see the need to observe certain courtesies, but they are the exception not the norm.