I presume you mean the emails you are sending bouncing. There are numerous reasons not handling bounced emails might be bad:
1) Waste of resources sending emails to no longer existing email accounts
2) Recipient mail servers may start treating your emails as spam
3) Depending on who you use to send emails you may find your email being deprioritised or being kicked off the service completely if the % of bounceback breaches a threshold.
4) In the unlikely event that the email is issued to someone else in future you may find yourself flagged as spam as the new recipient never signed up to receive them,