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Any turing complete computation system can be made to simulate another turing complete system.
~~All~~ Most modern programming languages are turing complete.
The Wikipedia article you linked literally has a section called "Non-Turing-complete languages" that lists multiple non-turing-complete programming languages
Yup, I made a mistake, should have thrown a 'most modern languages' instead. Oh well, my bad! As a silver lining at least someone on the internet got dopamine from a technical correction, so I already did my charity work for the day :)
Honestly, modern isn't even relevant in that context. It's easier to make a useful tiring complete language than a useful tiring incomplete language. It's not like as time went on we discovered how to make tiring complete languages more easily. If anything, we stumble into more and more things that are turing complete as things go on because it doesn't take too much for it to be, things like video games and board games.