Wouldn't it be safer to have a contract with an external backup company, just in case all your backup systems fail in the data center?

Yes. If you are running critical applications you should have the backup in different datacenter. Also, I would recommend you to have disaster recovery site as well. It is cheap nowdays, back in those days very expensive to have disaster recovery sites.

Do these backup companies charge a lot of money for their services? How convenient is to start up such a company?

We run multiple data centres for this very purpose and offer this as part of a package.

A customer simply takes systems in both locations and we can then configure up replication etc..etc.. I wouldn't say it's that costly either. If it's critical to the business, then work out what the real impact on the business would be in a failure scenario and whether it would be worth investing that extra money.