Uninstallation leads to broken system

Steps to reproduce:

- Have Ubuntu installed.
- Install lightdm. This makes lightdm the active window manager, as far as I can remember.
- Uninstall lightdm.
- Reboot.

Expected result:

- System booting another available window manager (gdm3 in this case).
- At very least an error message about something being broken (might belong to another package).

Actual result:

- System boots, but doesn't proceed up to visible graphics -> blank, black screen.

Diagnosis:

- One can still switch to a text console using Ctrl-Alt-F1..F4
- /etc contains a broken link (took me 2 full days to find that):
$ ls -l /etc/systemd/system/display-manager.service
... /etc/systemd/system/display-manager.service -> /lib/systemd/system/lightdm.service

Manual fix:

$ cd /etc/systemd/system
$ sudo ln -sf /lib/systemd/system/gdm3.service display-manager.service

Suggested fix:

- lightdm making another window manager active on uninstallation, just like it becomes the active manager on installation.
- Printing a big ERROR message if there is no other window manager installed.

ProblemType: Bug
DistroRelease: Ubuntu 20.04
Package: lightdm (not installed)
ProcVersionSignature: Ubuntu 5.4.0-29.33-generic 5.4.30
Uname: Linux 5.4.0-29-generic x86_64
ApportVersion: 2.20.11-0ubuntu27
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: ubuntu:GNOME
Date: Mon May 11 22:18:02 2020
InstallationDate: Installed on 2016-05-04 (1468 days ago)
InstallationMedia: Ubuntu 16.04 LTS "Xenial Xerus" - Release amd64 (20160420.1)
SourcePackage: lightdm
UpgradeStatus: Upgraded to focal on 2020-05-03 (7 days ago)