The desktop has the luxury to afford not being as secure as your phone, which serves as a 2FA device, a digital wallet, something that can record your voice and location, and your main means of everyday communication.
Side-loading would just mean every person getting nagged or strong-armed to side-load alls kind of apps (from official stuff from major companies wanting to avoid Apple's pay-cut, to all kinds of shady BS), with average Joes and Janes getting their phone smashed with malware, spyware and such.
The app store review doesn't have to be perfect or catch all. It just needs to be better than no review, and it does fare majorly better than Android (e.g. studies showing the latter gets 90% of the mobile malware).
The app store process and notarization also means apps can be revoked.