When BT receives a job complete ticket from the openreach engineer their system should automatically do a line test to confirm the job, and then upon failure pass it on to a team member who can at least contact the customer and reconfirm visit dates, or at best contact the openreach engineer that did the install and say it failed.
It seems there are plenty of issues on this forum of people's infinity being installed and not working - phoning customer services who do a line test to find a fault on the line. Why not skip the customer having to call? 1 line test per install cannot be an expense surely?
If the test itself is expensive, perhaps a check after 30 minutes if no internet used then do test.
It seems bizare that this doesn't already happen