Many of these arguments apply also to GUI "thin-client" type of terminal. The case for such terminals is frequently being made today and promoters are devising new slogans and names in an attempt to market the modern terminal concept under another name. For example "Cloud Computing".
PC's are so powerful today that just one PC can often support several persons using it at once, especially if they are doing low-load tasks such as text editing, data entry, etc. One way to do this is to connect a number of terminals to a single PC (or other host computer) by modems or direct cable connection. To do this, it's usually best to have a multi-user operating system such as Linux so that each user at a terminal can use the computer independently. This has been called "time sharing" but it's not good terminology today since "distributed" computing over a network is also a type of time sharing. It might be better described as "centralized" computing. But the central computer may be connected to the rest of the world via a network so that terminal users may send email, browse the Internet, etc. So it's not exactly "centralized" either.
Prior to about 2000, terminals were seldom used with PC's because the popular operating systems used for them (Windows, DOS, and Mac) were not multiuser until 1998 (available for MS Windows NT) and previously could not support terminals very well. Now that Linux, a multiuser operating system, is freely available for PC's, the use of terminals with PC's becomes more feasible. While text terminals are not smart enough to support the type of graphical user interface (GUI) that most computer users today expect, thin client type terminals are.
When Computers (including PCs) were quite expensive, lower hardware costs was a significant advantage of using terminals. Today with cheap PCs, the cost savings is problematical. I wrote the next three paragraphs years ago when PCs were more expensive. They are still valid today but of less significance:
If several people use the same computer as the same time, there is a reduction in the amount of hardware needed for the same level of service. One type of savings is due to code sharing. The application files on hard disks are shared as well as shared libraries in memory (even when people are running different programs provided they use some of the same functions in their code). Another type of savings is due to reduction of peak load. The hardware of a single PC may be idle most of the time as people slowly type in information, think, talk, or are away from their desks. Having several people on the same computer at once makes good use of much of this idle time which would otherwise be wasted.
These savings are substantial. One may roughly estimate (using statistical theory) that for 9 persons (8 terminals & 1 console) the shared PC only needs only about 3 times as much capacity (in memory, disk storage, CPU power, etc.) as a single PC in order to provide the same level of service per person. Thus the computational hardware for such a shared system should only cost about 1/3 as much per user. However, the cost of the display hardware (CRT's, keyboards, video electronics, etc.) is about the same for both cases. The terminals have the added cost of requiring additional physical cable connectors (such as serial ports) at the host computer.
For a fair comparison with PC's, the terminals should have the same capabilities as the PC monitors. Unfortunately, color graphic terminals for Linux (X Window) with high speed communication cost about as much as a PC so in this case there not much (if any) savings in hardware costs. But for text terminals there will be some savings, especially if the terminals are obtained used at low cost.
For centralized computing, software (and the updates to software) only need be installed and configured on one host computer instead of several. The person in charge of this computer may control and configure the software which is installed on it. This is advantageous if the person controlling the host computer does an excellent job and knows about the needs and preferences of the other users. Users can be restricted in playing games or surfing the Internet, etc. Whether or not centralized control is desirable depends on the situation. It's in a sense depriving users of their "right" to controls what they do with their computer including things that would improve their efficiency at work and/or entertain them.
With terminals, the computer hardware upgrades take place on only one computer instead of many. This saves installation labor effort. While the cost of the hardware for the host computer upgrade will be more than that for a single PC (since the host needs more computing power than a PC), the cost will be significantly less than upgrading the hardware of a number of PC's being used instead of terminals.
Text terminals are technologically obsolete because for a slightly higher cost of hardware, one can build a smarter terminal (with the same quality of display). This wasn't always the case since around 1980 memory cost thousands of dollars per megabyte. Today with low costs for memory and processors, one could turn a text terminal into a GUI graphic terminal for only about a 10% or 20% increase in hardware cost.
Since a PC can emulate a terminal, almost everyone using computers had a terminal emulator available until PCs started removing the serial port from new models during the 2000-2010 decade. You might think that now text terminals would be more in demand since emulating a directly connected terminal is only feasible with newer PC's (with no serial ports) only if one purchases such ports. But if one wants to connect text terminals (including emulated ones) to a PC via the serial port they will be out of luck if the Linux PC doesn't have a serial port. Thus the disappearing serial port tends to make the text terminal even more obsolete.
The reasons that text terminals are (or were) not fully obsolete are: