You can arrive in Dublin Airport and lose your passport somewhere between the plane and border control and still be let in.
You send the migrant back over the border, they get on another bus and get past the checkpoint the next time.
It would seriously inconvenience all the people who cross the border everyday and have been doing so for years.
The much fought for all-island economy and socio-economic links between North and South are even more developed now than they were during the Troubles.
People do not want to go back 30 years and we would be an international laughing stock all over some asylum seekers.
How exactly are you going to patrol all the many back roads and fields that crisscross the border?
They can across the channel in a small dingy so it would not even be a challenge to them.
We once had 2 highly armed armies and 2 police forces trying to stop people crossing the border for 30+ years and they couldn't stop it.
Any small few checks would only be tokenistic and more importantly ineffective.