There is no obligation on any country following the Westminister model to follow the precedents of other countries also having similar system. In fact, it would be an affront to a country's sovereignty if they were obligated to follow such precedents.
That becomes quite apparent when you consider how countries who have the Westminister model of parliamentary system themselves differ. For example, the original UK model that is still followed there doesn't have a constitution while other countries who have adopted it opted for a constitutional Parliamentary system.
On controversial democratic issues, politicians sometimes do try to argue that other democracies have a precedent of doing something in a particular manner and so there is nothing wrong in adopting it.
For example, some years back the Indian government run by PM Narendra Modi tried to amend the constitution to create the National Judicial Appointments Commission (NJAC) that would be responsible for the recruitment, appointment and transfer of judges, officers and other employees in the legal services. The government argued with critics of the bill that this was modelled after the British Judicial Appointment Commission. This was even argued in the Supreme Court of India when the constitutional validity of the bill was challenged. The Supreme Court however disagreed with the government and struck down the NJAC Act as ‘unconstitutional and void’.
Another example, that succeeded, is the anti-defection bill in India that allows a party to propose the expulsion of an elected party member from the Parliament if they violate a whip. The whip system of the British that allows a UK political party to expel a member from the party (but not the Parliament) for going against a whip was often cited in the public to push the anti-defection law.
But countries with democratic spirits do tend to observe and learn from each others practice.
For example, in the UK the monarch's role is now treated more and more as a typical head of the state whereas before they played a more politically active role. The old UK laws give a lot of power to the monarch that has since been diluted by legally interpreting it more and more narrowly to mean that the powers are still bound under democratic terms and not absolute. Indian political parties have been considering reserving Parliamentary seats for women, inspired by Bangladesh where women reservation in Parliament has existed for sometime now.