I frame my own disdain for SaaS along three axes:
1) Control - SaaS usually ingest my data and silo the results of my work, so that I don't own the output. This is often unacceptable. It also makes solving problems harder. With a local application, I can always hack around its deficiencies, or easily post-process its output. Can't do that with a webapp owned by someone else.
2) Reliability - While a SaaS will be more incentivized to support a paying subscriber, pay-once software with no auto-updates is more reliable once it solves your problem. That's because it's frozen in time. It doesn't get new features (which usually aren't needed if you have a working solution already), but it also doesn't break. In the context of your whole computing system, pinning to a version of a local piece of software lets you freeze one component of your system - which reduces complexity, and gives you one less thing to worry about.
(Longer term you may need to worry about the rest of your system becoming incompatible with the version-pinned program - but VMs essentially solve that these days.)
3) Relationships - Every SaaS I subscribe to is another relationship I enter with a third party that needs to be consciously tracked. I don't want that, it's anxiety-inducing and cognitively exhausting in the long run. What I want is to pay money in exchange for solving problems. I don't want new relationships on top of that. I tend to use the following example: when I go out to buy some bread in the morning, I exchange money for bread, and that's it. I don't enter into an ongoing relationship with the store, the bakery, the flour supplier or the wheat farmer. I like my software like my bread.
(To be more accurate: I actually do enter into a bunch of relationships when I buy food or trinkets in stores, but they're all governed and fully handled by various business and consumer protection laws - which means that I don't have to care about them. They only matter if something goes wrong with the goods I bought - and then all I need is to keep a proof of purchase and know who to e-mail about it, and I can even CC the government to force-handle things for me. Meanwhile, SaaS creates relationships you do have to track yourself.)