The phrase 'demand grew' is correct and usable in written English.
You can use it when you want to express an increase in demand for something. For example, "The demand for electric cars grew significantly in 2020."
"We just grew as demand grew".
As demand grew, so did production.
After the gulf war, demand grew.
Demand grew, and plantations sprouted in Malaysia in the 1930s.
Eventually demand grew, and the family added more sewing machines.
As demand grew, hotels began raising room rates.
Schlumberger's latest earnings report, in January, predicted that its businesses would improve as energy demand grew.
The extension could take place a runway at a time as demand grew, or financing allowed.
As demand grew, however, new methods were devised for evaluating the potential of underground rock formations.
As demand grew, the cartel constructed superlabs, capable of churning out industrial volumes of meth.
Retail sales, which give an indication of domestic demand, grew 13.1 percent in July.
