"demand for better" is a correct and usable phrase in written English.
It typically expresses the idea that something should be improved upon. For example, "The workers demanded better working conditions."
While flights got cheaper, demand for better facilities pushed up the cost of boats.
The general use of automobiles created a strong demand for better highways.
Yet the demand for better robots in Japan goes far beyond such functionality.
And this, in turn, "created a demand for better nocturnal lighting".
Yet it may increase popular demand for better enforcement of existing laws.
It is thriving, reflecting strong demand for better schools than the state can provide.
As smartphones fly off the shelves, demand for better mobile internet will go through the roof.
Builders are responding to the demand for better and bigger bathrooms.
These factors created an incessant demand for better roads, and supply and invention both rose to meet that demand.
The resulting demand for better textiles caused the industry to outgrow the peasant household means of production.
If he can aggregate their demand for better financial services, this large population could create an impressive business.
