I think the service aspect of *aaS businesses is literally half the game. Yes, you are delivering a product but the service aspect involves the monumental task of maintaining servers, maximizing uptime, being sensitive to security and anything else I've missed. If you want your product to have 100% uptime, that's the service you are performing.
In my opinion, being "up" is just a prerequisite. If your aaS business is technically not viable you'll just not make it. Support and client account management is really important to succeed. aaS is "self-service" - so when a client or prospect has a question about the product, an answer must be provided efficiently, and that is a differentiating criteria...