This is not how the world already works.
If CBP's systems go down, they will not process (foreign, they'll process US citizens still) arrivals [1], even with physical passports in front of them. I assume the EU ESS works the same.
"If the internet goes down, your border checkpoint is down" is not some terrifying future we need to protect against, it's the reality of the world as you live in right now.
[1]: I've had to wait for an hour, at SFO of all places, because of exactly that happening.
TBF given that a temporary outage is abnormal it makes a certain amount of sense to default to shutting down. Whereas during an extended outage you can pick back up as long as the key parts of your system are capable of operating without the network.