Upvote:1
No such meta search exists that’s focused on taxis but you can do an equivalent search in App/Play Store. For example “taxi Barcelona iOS” yields a link to an app called Free Now that does what you want as they’re only partnered with local traditional taxi companies. From personal experience I can say the app was horrible as of 2019 (compared to Uber/Lyft) but perhaps they’ve improved since then. In Czech Republic an equivalent service is called Liftago and is likewise easy to find in app stores.
The only real “meta search” is Uber/Lyft but since you’ve explicitly excluded them, App stores are your best shot.
Upvote:2
Meta-search engine for licensed taxis.
One can use taxicaller, which claims to support over 70 countries.
With that being said, those "traditional" licensed taxi networks are typically very limited in coverage, overpriced, messy, inconvenient, technologically subpar, and sometimes dangerous, which is why ridesharing companies have rapidly taken over in pretty much all countries: in most reasonably developed places, Bolt/Didi/Grab/Lyft/Uber are available. Your choice.
Upvote:4
I think you've kind of answered your own question here:
Ideally, I'd just let my presence known through a smartphone application, and then whichever taxi company claims me first would come to fetch me.
This is pretty much exactly what Uber, Bolt etc do, only instead of a "taxi company", you get a notionally independent "driver-partner" to claim you. Now I know you stated that you will not consider "any unlicensed, unmetered, or illegal taxi operator such as one is very likely to get with such services as Uber", but the regulatory situation in Europe (and the rest of the world) has changed since the early wildcat days and ride share operators are very much licensed and regulated these days, often including employment-type protections for their drivers. In Spain, specifically, all Uber drivers have been licensed since 2016.