The phrase 'higher status than' is correct and usable in written English.
You can use this phrase to compare two items, people, or things. For example, "She was given a higher status than her colleagues."
The fish chef will often, unofficially, have equal, if not higher, status than the sauce chef.
"They were doing altar pieces, which were considered higher status than just portraits.
Why should universities have a higher status than further education colleges?
Males enjoy higher status than females; boys are often pampered while girls are relatively neglected.
The Mongols provided artisans with a higher status than was the case in many societies.
Under Mongol rule, merchants had a higher status than they had in traditional China.
Greene was well aware that the prodigal son has a higher status than the loyal stay-at-home.
I also knew that African-American entertainers often had much higher status than white visitors to vice districts.
Teachers in Gymnasien enjoy a higher status than those at other schools.
They are less likely, however, to return the smiles of people they consider of higher status than themselves.
There is also a debate to be had around giving traditional methods of campaigning higher status than others.
