Perhaps this explanation will help. When I hear the word 'Sahara' I think of a physical place, in northern Africa. When I hear the word 'desert' I think of an ecological system, characterized primarily by low rainfall and sandy soils. When I think of the physical place in northern Africa that is denoted (in my language) by the word 'Sahara', I think of it as being an exemplar of the ecological system denoted by the word 'desert'.

Near me, there's the Sonoran desert and the Great Basin desert. If I lived in eastern Asia I might think of the Gobi desert. There's many deserts. So while I take your point that 'Sahara', in a non-English language, denotes what I call in English 'desert', I would say that the phrase 'Sahara desert' could be interpreted to signify "the place on this planet, that could be characterized as having a desert ecosystem, that is described by the people who live nearby as 'Sahara'". For the people who do not know that 'Sahara' is used by some other people to denote what they think of when they say the word 'desert', the word 'desert' is not extraneous. But for you, who does, it is.

That prompted me to look up what 'sahara' and 'desert' are in Arabic -

صحراء - Sahra' - Desert

الصحراء الكبرى - alsahra' alkubraa - The big desert?

What language are you coming from?

The same reason English speakers often say “chai tea”.

They speak English, not Arabic or Hindi, and those words haven’t been turned into loan words. Likely, because English has its own equivalent.

Because there are many deserts, and the Sahara desert is just one of them. There is the Gobi desert, Mojave desert, Kalahari desert etc.