What about infrastructure costs? Are you comfortable making someone else pay for your access? What about the design and implementation of the API? Should all software be free?

Please note that I’m not trying to support this decision at all. I personally feel like API access is similar to SSO for enterprise stuff (check out sso.tax). I also feel like there should be some level of compensation and even profit so people can focus on building stuff like this. It’s really hard to define what that is, especially without transparent costs, which I don’t believe OpenSubtitles shares? Also they use super predatory ads so I don’t think they have any high ground to even suggest what I’m talking about.

I'm paying for the fact it's popular with submitters so has the most subs available (this could change with the recent announcement, we'll see) and an API that allows automated download of subtitles including matching of the scene file that is being played, supported by Jellyfin/Plex.

Is there another, free, as popular resource with an API? If so, please share.

No work? They host, maintain and provide access to a massive catalogue of subtitles providing metadata needed for matching media to subs and up until recently we're giving free access to everyone. Might I suggest if you care about your wife's access to subtitled movies this much that maybe you should buy the 10 euro per year subscription for her to help keep the platform alive? Alternatively you can find a subtitles group that does all this for free and choose to solely download their subs (also I assume donating to them since you're so appreciative of their work).

He can put that subscription right up there with his Youtube Premium

True, but some scene members strip the subs from the media, although it's getting rarer these days.

I also use Bazarr to fetch SDH subtitles which include subtitles for background sounds and the names of who is talking.

I agree that ideally subtitles should be included on all, but we don't live in a perfect world.

They often do not include many languages, sure if you want English subtitles it's likely they will be there. But good luck getting subtitles for movies and shows that didn't have an official in the given country.