There are so many logistical problems with this, though:
If schools recruit extra temp staff, who will DBS check them in time?
If school staff are doing it, who is teaching live lessons, teaching the kids in school, supervising key workers/vulnerable, dealing with normal pastoral issues and so on and so on.
How are these kids going to get into school? Many students rely on busses or parents dropping them in. If they're coming in for a test appointment, how will this be possible?
How do we keep all the kids isolated from each other, and what happens if one does test positive?
How do they get home again quickly afterwards (so they are not all hanging around on the school site)?
What happens if parents refuse consent, or the student can't be tested at the time? Do they just not get to come back to school?
If staff are being exposed to positive cases at close proximity, what happens in the second week of term, when they are all off ill?