If you haven't experienced this ever, definitely be extremely grateful. Also, when you switch jobs, beware that past experiences are no guarantees.
I'd personally be very suspicious of anyone who tells you not to do that. There is literally no downside unless you're trying to hide something.
It has happened many many times that I thought I was clear on a thing and that everyone was on the same page to later realise that some of us completely misunderstood what was discussed or agreed. Sending a summary email afterwards helps make sure that everyone came away with the same conclusions.
I’ve also found it extremely common that people simply forget things, or parts of things. I’ve had bosses who forgot that they asked for a change or feature or task to be completed. I’ve had bosses who forgot that they agreed to change a requirement or that something isn’t needed or important. I’ve forgotten that I said I’d get something done. I’ve had coworkers forget that they were supposed to do certain tasks.
By sending a quick “here’s what we agreed to” email avoids all of these issues, or, at least, let’s you point at it later if someone questions it later.
Basically, it’s a good idea to keep a log of decisions that were made.
But anytime I've suddenly been stuck feeling "wait how was I doing the wrong thing?" the overwhelming reason has been traceable to the fact I can't point to any specific bits of correspondence which justify why I was doing something a particular way because it was all ephemeral.
For me, it's a workplace confidence builder - there's not a lot of light between a manager forgetting something you said, or hearing something different, from your perspective when the question posed is "why did you do a thing?". In those moments, being able to point to specific records of correspondence means the discussion now has a concrete starting point - even if it's going to turn out you absolutely misinterpreted what was asked.