Is it true that good managers should first come to work and be the last to leave?

It depends on the nature of work and complexity. I does not necessary for manager come office early and depart late. Manager must have work plan who will do it as well as he will be accountable to complete the work right time. Manual manager takes a lot of work stress and does not interest to delegate power and authority. However, manager must have discipline and role model for his or her supervisee.

Time management and work discipline remains same for all and teaches all to be in time and leave in time. 

In reality, YES. 

Not necessary. Staff can work well without having a manager in the office.

Not necessarily.  While it can be a good example that a manager should lead by example - that is reporting for work on time, it does not necessarily follow that he/she should leave the office later than others do.  What if he or she has to attend to business transactions or meetings outside the office before office time ends? Rather, good managers should be measured by the quality of work or performance he/she puts into the job.

Even if Manager is absent in the office, the office itself should feel the presence of Manager.

Manager must be exemplary in the application of labor laws, a good example for his employees

First of all , It’s not our concern (According to my opinion & experience ).

Secondary : No, It is not necessary.

 

Surely yes

it is not necessary that to adhere this policy regularly. however the arranement and implementation of formalities to follow the descippline in department completing the task without constant followups is the strategy plan.