Some companies think that some people don't know what the numbers mean on the bottom edge of the check. Therefore asking for the check means that the company can get get the numbers from the check/image. The percentage of people who can't get this information from the bank website, is decreasing over time.
Having a check to send does imply some level of assurance that the checking account is real, and connected to the name. This is becoming easier to spoof over time, so it might not provide any guarantee.
If you have a check it means it is a checking account. The company knows it isn't a savings account. In some systems this does seem important.
Asking for a check was a typical thing employers did when bring onboard a new employee. They did this to setup direct deposit. Now asking for it for payroll is rare, but one family member did need a voided check for a position started about 5 years ago.