Not allowing staff members to speak among themselves even for two minutes is height of close and tight supervision. This type of management style was prevalent Europe and USA when industrialisation begun.
Now a days lot of talk is going on whether robotisation will impact the work. However, your management has converted humans into robots. Possibly yours could be only the company where robotisation will have no impact!
Now coming to solution. You have written that you work in service industry. What type of services your company provides? What type of customers do you have? Do customers visit your company premises? In the service companies, interaction with the customers is ongoing process. How the interaction takes place? Is it face to face or through email or through telephone? Because of the 2-minute breaks, will the customer service impact?
Interaction or no interaction amongst the staff members, a service company needs to measure the various ratios to measure the business performance or customer satisfaction. How do you measure the customer satisfaction? What are the parameters? How the business performance is measured?
In all types of companies, teamwork is needed. To foster the teamwork, if not emotional, at least professional connection is essential. Why your management is so rigid about the interaction among the staff members? A workplace of 21st century is different. Companies invest heavily in employee engagement activities. As a part of these activities, some games are also conducted at the workplace. From the discussion that follows after the games, exchange of views takes place. Contrary to this, why your management has taken a inflexible stand that can be compared with the management style of 19th century or first half of the 20th century?
Yes, working under very close supervision is difficult. It will be unbearable if the person is outgoing, sociable or lively. However, what about the other team members? Is this diktat of the management acceptable to other members? Have they expressed their dissatisfaction?
One of the solutions could be to organise the town hall meeting and employees express their reservation about this forced quietness. If inflexibleness of the management continues, then quitting the job is always the solution!
The other thing I would like to know, is whether there is an actual complaint from the employees in this regard