"we should demonstrate" is correct and usable in written English.
You can use it to suggest that an action should be taken as an example of something or to prove a point. For example: "We should demonstrate our commitment to sustainability by using reusable packaging materials."
"We should demonstrate how transparency does change behaviour.
Perhaps we should demonstrate to him -- and every other angry young man like him -- that we aren't scared of his dumb Internet rhetoric.
We should show our own strength and belief in the values of democracy and tolerance, and above all we should demonstrate that the future, however hard the path to it is, does not, and never will, belong to fanatics but will be with those who believe that we should live in peace with each other, whatever our race, nation, colour or religion.
Their nuclear ambitions and destabilizing behavior threaten both of our populations, and we should demonstrate the same resolve against them.
Respect is an obvious characteristic we should demonstrate in professional settings.
This doesn't mean we always need to be paragons of contented bliss, but we should demonstrate our ability to manage stress and respond, not react, to setbacks.
We believe accounts should demonstrate clearly that public funds have been used according to plan, and have been used effectively and efficiently.
We also emphasized that they should demonstrate how they read a research article and identify the moves (i.e., modeling).
We reasoned that exocyst mutants should demonstrate altered sensitivity to these hormone manipulations if the reduced root growth rate in exocyst mutants is primarily the result of a defect in auxin transport.
Bell: We think investors should diversify their portfolios, and emerging markets over time should demonstrate less correlation with developed markets.
We propose competency statements that an effective interdisciplinary team functioning at a high level should demonstrate.
