That's true as far as it goes, but there are plenty of other reasons it's become so prevalent.

From a vendor's perspective:

- Web apps often have a reduced support burden relative to equivalent desktop apps because you have easier solutions for complete control over deployments: environments, live versions of software in play (often only one).

- Subscription payment models are convenient for vendors: they can help smooth out revenue but, critically, can also increase lifetime value of customers.

From the customer's perspective:

- One less software system to deploy, manage, and support,

- Managing backups is (should be!) taken care of for you,

- Lower on premise hardware costs,

- Your stuff is available from anywhere you have access to a browser,

- Can enable frictionless collaborative working.

With that said, it's arguable that a purely web-based SaaS model isn't necessarily a good fit:

- The problem of lock in is often worse. Even if you have options to export your data, is it in a format that makes it easy to import into a competing offering?

- Poor (or no) offline support, and unreliable operation with choppy connectivity.

- TCO can be higher, despite reduction in on premise support costs.

- Subscription payments can quickly mount up to death by a thousand cuts with respect to costs.

- Your data is not only offsite, but may not be stored in the same country or even on the same continent: a deal-breaker in some scenarios.

- Susceptibility to attack via DDoS, and other methods: at best service can be degraded or rendered unavailable, at worst your data can be compromised.

SaaS is like anything else: it can work really well (Office 365[1], GitHub, GMail), or it can be decidedly ropey (Google Docs), or anywhere in between.

[1] Within certain constraints - to me Office 365 still feels weak as a collaborative tool.