The reason I stated the premise like this is because in my experience that is generally how new people are brought into a group. Basically an established player meets or knows someone that wants to play, there is an opening in the campaign (like starting a new campaign or a great spot to enter a campaign), and then they invite them over.
But all of that is beside the point. I have seen this example happen, and I have also been the person brought in. I have never, in my 40 years of being a DM or player, not seen at least one limitation set by the DM. Sometimes it's about backstory, other times it's about not allowing spells or classes, other times it's about not allowing a species, and other times it is about not allowing a certain rule. I have seen the reverse true too, giving players extra additions to their backstory, extra spells, extra classes, extra species, etc.
But this example is just a common way people join a gaming group. The host and DM are different people. It is a simple yes or no. There is no judgement on my part. I just want to see what people think.