If you have a mail program on your computer poll both accounts, instead of Yahoo downloading the email into a combined account, a Yahoo service outage or something else such as your Yahoo account getting hacked won't impact your ability to get at your university emails.
Most likely your University has better email support than a free Yahoo account.
If something happens to your Yahoo account the emails in that account could be lost forever.
If there is any sensitive or personal information in those emails it could be used against you or the students.
If you are downloading all email to your computer I recommend setting up an
online backup service to protect the emails (and your other files too) in case something happens to your computer.