SorryWhat - I get there are a range of views on whether the detention was fair.
But I wish people wouldn't keep wittering that they'd 'refuse the detention'. You can't, unless your plan is that the dc just don't return to school ever.
School aren't asking your permission; they are telling you that that is what will happen. If your child doesn't attend detention then it'll just escalate to the next punishment, whether that be a longer detention with a more senior member of staff, isolation, or a fixed term exclusion.
Given that there are 315 messages debating whether this perfectly straightforward detention for lateness should occur in line with the school punctuality policy, you can see how it might be a bit time consuming if every single lateness excuse required this level of scrutiny & debate before the kid actually attended a detention!
& also quite a bit more unfair if child A's parent gets to phone up & say 'lol nope, my child isn't doing it' whereas child B's parent says 'oh how annoying, dc! But you'll have to suck it up.'
Which is why if the school leadership know what they are doing, they categorically won't take any nonsense about whether the sanctions apply in every individual case where a minor household cock up led to lateness/lack of kit/no homework etc etc.
Most of us would be bloody glad of a school that consistently imposes coherent, well understood & fairly applied sanctions when it comes to dealing with students who disrupt our own dc's learning.
A bit of accepting that in the real world, for school sanctions to rain on the unjust, sometimes they also 'sprinkleth lightly on the not really all that unjust' is the only way to establish that, unless you're proposing that each school has at least one member of staff whose full time role is to triage level of parental disgruntlement & respond to it.
My own school has adopted a 'no excuses' detention policy on lateness. In September, when it was introduced, there were probably a couple of kids in most classes affected every day.
Now, in February, we get an email if any student is late. It's usually 2-3 a week.
Admittedly our detention for a second offence lateness takes place at 7am
so kids tend to get the message after the first, after school one...