Unless it's a trusted recommendation I'll look on the app store first. Sometimes I'll still get it from the app store anyway:
- The store itself is convenient for browsing and discovery.
- I don't need to do any kind of background checking on the developer prior to running their app
- Similarly they don't get access to my credit card details, so I don't have to be concerned about them storing it incorrectly or abusing it later
- It's also easier for me to pay them, as often foreign transactions are blocked despite me specifically approving them.
- I don't need to hand over my email or other personal details, small developers seem really bad at storing information and CC details properly. I use custom emails for everyone and numerous times I've seen my data on-sold, stolen by ex-employees, or simply thefted from the company by hacking groups.
- I don't have to do any reviews when there is an update, I can just accept it knowing that the developer is still trusted and that the project hasn't been hijacked such as the numerous painful times that popular open source projects have had malware snuck into them.
- If the app doesn't properly do what claims (or at least what I thought it would), it's a few clicks to get a refund from Apple.
- Apple carrot and stick developers to keep their apps up to date with the system. First carrot, and eventually the stick (delisting).
Some may argue that some of these things can still happen with an app store, but it's demonstrably less and there are processes in place to deal with that.
It's not a popular opinion, especially on HN, but there are plenty of developers who, whether through frustration or dealing with pedantic/rude* customer requests, treat their customers like shit, the store prevents that.
The app store ain't perfect, and there are plenty of functions which apps can't have if they're sold through the app store, but for its flaws it's trustworthy and helps me utilise a far larger number of utilities than I'd normally be comfortable with personally maintaining.
* I sit on enough discords to see how breathtakingly rude and demanding some users are without noticing it, even for totally free software.