The purpose of backing up a computer system is to ensure you have the most complete, consistence and accurate copy of files as possible as a set.
Backing up a computer system should be done at a time of day that results in the fewest files and users being impacted. Most small/medium companies back up their files late at night to ensure the highest accuracy, completeness, and consistency of data sets.
Backing up systems during the day or just after the normal end of a business day can result in some files not getting backed-up for days if they are files that are updated continuously during the day. Open file agents are still not 100%. It is important to remember that the purpose of a backup is to have an accurate copy of files in case a restore of a file or an entire system is required.
A backup schedule late at night means the fewest users and files impacted. It is important to remember that a backup done during a business day impacts users by slowing down response time and files, and results in an incomplete backup. Some data sets are spread among multiple files, if they are not backed up with the same consistency state, then they are as good as corrupted, a typical example are databases.
The scheduling of a backup isn’t when it’s convenient for the system administrator, but when it’s best for the specific business. I have heard of system administrators setting their backup schedule so that they can see it start (tail wagging the dog).