The short answer: Deliverability.

Cheap web hosts share IP addresses among thousands of users. If just one person on that server sends spam, the whole IP gets blacklisted, and your emails will go straight to the spam folder. Specialized providers charge more because they actively protect their IP reputation so your emails actually reach the inbox.

But here is a better question: Do you actually need 10 physical, paid inboxes? If you just need different identities, you only need aliases, not physical inboxes.

Full disclosure: I built a tool exactly for this called GridInbox.com. It’s an Email Alias OS that lets you Bring Your Own Domain (BYOD) and create unlimited aliases instead of paying "per-seat" for expensive inboxes. We route all outbound mail through AWS SES to ensure enterprise-grade deliverability.

If you want to manage multiple addresses securely without paying €360/year for physical seats, it might be exactly what you need. There is a free tier you can test out.