Translation:I ride taxis.
One reason is that even if you don't know a word, if you know the kanji used to write it, you can often tell what it means. It's like how in English knowing the Latin or Greek roots of a word can be helpful in trying to guess what it means. I often run into words in Japanese which I don't know how to pronounce but I know correctly what they mean because they're written with kanji.
The main reason though is visual clarity of meaning. Once you recognize kanji, they stand out from the kana and help you know what's being said more quickly without having to pronounce everything. Part of the trouble here is just that Japanese tends not to use spaces between words, so without kanji it can be hard to tell at a glance where words begin and end, but also there are a fair number of homophones - I sometimes think Japanese even outdoes English when it comes to puns.
Kanji help to clarify meanings while adding visual contrast to make sentences easier to parse. It might not be the best system, but it does have its advantages.
It's also worth noting that Chinese characters are built out of parts that get reused, so learning them is not much worse than learning how to spell words in English.
I'd just like to add that in my opinion learning kanji is definitely easier than learning English spelling: while you have to learn about the 2000 most used kanji in Japanese, English pronunciation is so irregular that in order to know their correct spelling you need to learn every single word, regardless of their grammatical category or roots
Another factor in that is that Japanese had a spelling reform in the mid-1900s. Before that, it used a historically-based spelling that wasn't nearly as close to how it sounds: https://en.wikipedia.org/wiki/Historical_kana_orthography
English spelling has a lot of history in it, and hasn't been reformed, which is a major factor in why it's so far from pronunciation.
the other comments are not entirely wrong but here's a more straightforward answer: typically you add は after に if the verb (in this case "ride") is in its negative form. (e.g. "I do not ride taxis" - "タクシーにはのりません") You usually don't add は after に otherwise, unless you specifically want to mark "takushii ni" as the topic, although I can't think of a case where it would make sense to do so.
Duolingo doesn't really do a good job of explaining verb negation or just particles in general. Here's a pretty good explanation of how you can use particles in negative form: https://www.learn-japanese-adventure.com/japanese-particles-change.html
は marks the topic of the sentence, which in this case is omitted. The full sentence would be something like [わたしは]タクシーにのります, "[I] ride a taxi", but in Japanese it's common to drop the [わたしは] as it's usually clear who you're talking about from the context.
This is different from the other sentence that I'm guessing you're thinking of, タクシーにはのりません, where the topic is the taxi. It's kind of confusing because it's a distinction we don't really make in English. In the first one it's like saying "Talking about myself, I ride taxis", while the other is "Talking about taxis, I don't ride them". I recommend reading about the use of は and が as it tends to be a concept that usually takes learners awhile to really understand. Here's a site that I think does a decent job of explaining it: https://8020japanese.com/wa-vs-ga/
Kanji came before kana so the Japanese didn't invent more complicated characters - it was the other way around. Kanji are chinese characters that the Japanese borrowed and changed for their own use. From Kanji they developed the more simplified hiragana and katakana (commonly referred to as simply kana) which have phonetic value only - ie. they only convey how something is pronounced like the English alphabet, and nothing else. Kanji however convey meaning AND sound and because they are borrowed from Chinese they have different "readings" or different ways of reading/pronouncing them - some kept or changed slightly from the Chinese pronunciation. Sometimes Japanese words can be written entirely in Kanji and other times they are written partially in Kanji and partially in kana. Because Kanji convey meaning as well as how to pronounce them they can be helpful especially if you don't know a certain Kanji. For example say a word is made up of two or more kanji you might not know one kanji but you might know the others and may be able to guess the meaning that way. Kanji can either be one character or two or more characters making up one character, so if you don't know a Kanji and it is made up of multiple kanji you might be able to recognise one or more of the characters that form that one Kanji and guess the meaning that way. I have a great Kanji book with several different ways to look them up - pronounciation in romaji, number of strokes, by radical - by the number of strokes of radicals. I think Kanji is fascinating.
Every Kanji character has its own meaning and pronunciation. If you replace 乗 with の, you only preserve pronunciation part of the whole information. It might cause confusion with some other words with same の pronunciation (e.g., 載る). Thus, in my honest opinion, it can be an elegant way to represent the origin and delicate nuance of a vocabulary within itself in a simple manner. (Disclaimer: I'm not Japanese, so I'm not sure whether they actually feel it in this way.)
Because if I say "はやいですね" it has meaning: "it is fast, isn't it" and "it is early, isn't it" but if I write "速いですね" it can only mean "it is fast, isn't it" and if I write "早いですね" it can only mean "It's early isn't it". It actually reads much faster, because the many strokes makes it more distinguishable, but both is said "はやいですね". Japanese is very context-dependant. When they say it, you can see the context clearly because if it is late and you are in a fast car it doesn't make sense to say "It's early" so then it only has one meaning. But in text it gives context directly thanks to the kanji. I hope this answer helps.
I agree that "I ride a taxi" is not natural sounding English, and gives the impression of riding on top of the taxi roof. Possibly the reason we "ride" a train or bus, but not a taxi, is that, traditionally, you had to step up to get on a bus or train, so you were in a sense mounting it like a horse. "I use a taxi" was not accepted as an answer to this question.
Translation from any language is tricky - Japanese is tricky I think because the Japanese conveys more than the English equivalent is able to - for instance 乗る can mean to get in/on, board, ride, ride in/on etc. This one Japanese verb conveys all these possible meanings at once but the English rough equivalent " I take a taxi" is comparatively flat. It just can't convey all that the Japanese does. So it's hard to show that you understand what the original Japanese is saying without sacrificing natural sounding English. I think this is why Duo has so many odd sounding English translations - I suspect this is not just the case for Japanese either, although I will say that because Japanese is able to convey multiple meanings at once it does seem to happen more in Japanese lessons.
Btw - うんてん する means to drive.