I experienced this issue and did resolve it (without the dual profile as suggested by @MPKRVA but that certainly did help me to my resolution).
Problem
To clarify, the process was working in the same way as the original post described. All VPP was setup and configured as desired (I had purchased InTune Company Portal via Apple Business Manager). After wiping the phone You go through a few screens, ultimately getting to 'This phone is owned by ###' and you must click enrol.
(When wiping, take care not to get caught by Activation Lock if its your first time. Make sure the phone is fully removed from any Apple IDs)
After enrolling and getting to the main screen, it was either right away or after one unlock that the screen and side buttons become unresponsive. You could wake the screen by turning it over and facing it back up but that was it. It was successfully connected as I could find the device in InTune (Devices > iOD/iPadOS), select it and select 'Wipe' to start the process again.
Resolution (with journey)
I created an Enrollment program token profile with 'Run Company Portal in Single App Mode until authentication' (SAM mode) set to 'No' and assigned the device to it. Running the process worked without the lock up but there was no guidance to log into the InTune company portal.
What I did receive is multiple messages trying to get me to sign in to an Apple ID. 'App Installation: Sign in to iTunes to allow ### to manage and install apps'.
I started looking into the App side of InTune and believe I discovered the issue. I don't have the exact screen shot of it now as its fixed however, I had previously tried to add the Intune company portal app as an iOS store app that I would assign.
When you buy and app from the Apple Business Manager, the VPP token connector syncs and the app becomes visible in InTune in iOS/iPadOS app with the type of 'iOS volume purchase program app'. I removed my previous attempt with the type of 'iOS store app' and changed the assignment of the VPP instance of the InTune company portal to be assigned and assigned it to my devices.
After this the process worked as required. I still have several other hoops to get through now, enrollment goes to InTune company portal in SAM mode until signed in, and there is no lock up.
In the below picture.
Apple Books: This is set to uninstall for all but it will do nothing as it was not installed by InTune.
Intune Company Portal and Microsoft Teams: These are assigned to tall devices and do show up on them
Microsoft Word: Is licenced with ABM > VPP but is not assigned to anything so will not show up.
I do hope this is of help.