The pubs weren't allowed to open in Leicester as they had extended lockdown and that obviously didn't stop the spike there.
So school/pub is a false choice in my opinion. I totally understand the trade-off requirement but how about actually the government put some real work into finding out the environments where spikes are happening and why, and better controlling those.
Factories, shops, pubs, beaches, religious gatherings, airports, schools - all these places have their own demographic and dynamics and some will need controlling more than others but I don't feel enough work is being put in to understand this.