When I taught in the UK we had this - but it was used sensibly.
So if a student was patting about: first warning, second warning, time out THEN collected by on call behaviour manager & removed to the sin bin.
Each department had its own time out timetable; kids would be sent to a lesson being taught to a different year group, to discourage 'oh all my mates are in set 3, I'd quite like to be sent there'. We worked it out carefully so that the designated time out room was always the one with the best behaved class &/or sternest teacher.
If you were still being disruptive having been dispatched to top set y7 or whatever, then the teacher in that room would message the office & you would be removed to the isolation room.
Time out meant a detention. Isolation meant you were there for the rest of the day & the following day up until that lesson (so if your behaviour had resulted in isolation last lesson on Tuesday, you would only rejoin your peers last lesson Wednesday ).
If you found yourself in iso more than once in a term, you & your parents met with the Head before you were allowed back into classes. If you continued to be a pain, things started escalating towards exclusion.
It worked pretty well. Everybody else got to get on with learning without the disruptive element. Most kids were never in isolation, & those that were generally hated it & made sure it didn't re - occur.
We kept banks of subject specific work for students. Not perfect because there's only so much you can learn from a worksheet BUT if someone is continually disrupting lessons they aren't learning much anyway.
Sending kids to iso for forgotten pens is just silly. I pick up every pen left on the floor or on desks & keep them in a jar on a side table with dictionaries etc. If a student rocks up without a pen, they know the deal is that they are welcome to take one. If they do so as soon as they enter & don't disrupt anyone by faffing about trying to borrow one, or expecting me to deliver it to their table, we're good.