In the beginning (this is sounding Biblical) all computers had lights and switches. There are a bunch of reasons:
The early hardware was terribly unreliable. Tube-based computers were constantly failing and the fastest way to troubleshoot was to see indicators for all the bits flowing through the various subsystems.
Software bugs could be tracked down by single-stepping a program manually and watching registers or memory locations for expected results.
Indicators and switches were often used to enter data and even programs by hand. This was a step up from plugboard based programming since changes were much quicker.
Blinking lights were impressive. If your organization had spent 100's of thousands or millions of dollars on a computer system, showing off all that activity to people was a showcase, even if they hadn't the foggiest notion of what all those blinkinlights meant.
Computer operators had a certain mystique they liked to maintain. They could impress their bosses by quickly tracking down faults, even when computers became more reliable. Things like stuck bus bits (either 1 or 0) could be traced.
Computer systems did not have sophisticated consoles; they had simple mechanical devices like Teletypes or Flexwriters and there were no build-in monitor programs to do interactive examine/deposit commands from the console. These came later with the advent of ROM-based boot loaders and microprocessor based subsystems.
Early computers were hand built. During the assembly process, it was necessary to have switches and lights to verify all subsystems and correct mistakes like wiring errors. Removing anything not needed for operational status would have been an added expense, so it was more effective just to have them as part of the design. This was also important for future upgrades and modifications, which were frequent. The PDP-1, for example, underwent at least 4 version modifications by both DEC and its customers.
The main problem with all those lights on the early systems was that they were incandescent (and sometimes neon), which meant they burned out and had to be replaced. A burned out indicator meant you could not tell whether a bit was a one or a zero. Almost all computers using incandescent bulbs had a lamp test button which would allow a maintenance technician to replace the dead ones.
When LEDs became widely available and cheap in the early 1970's computer makers began to replace incandescent indicators with them. This relieved a major maintenance headache. I recall some early DEC computers with incandescent bulbs - some were even soldered in place so you had to remove the panel, unsolder the dead bulbs and solder in new ones. Standard operating procedure was the give the panel a firm rap to uncover any weak bulbs on the verge of failing then replacing those as well.
The early hobby machines like the Altair all had switches and lights. When the Apple came along, things changed.
So those of us who experienced all those glorious lights and switches, which gave us almost unlimited control of the machines, miss those days and this is what has fueled a resurgence of interest in replicas of those old machines.
As mentioned, Apple was one of the early home computers to not have lights. It either booted up or you had to get it fixed. Others followed suit and diagnostic indicators, if any, were flashing patterns or cryptic errors on the connected TV screens.
DEC began to phase out light panels on its minicomputers in the mid-1970s. DEC Field Service had a program to replace all PDP-11/70 computer front panels (those under a maintenance agreement) with a faceless "remote diagnostic" console. Many people (myself included) hated the idea. The advantage was that a remote service center could log into the customer's panel via a modem and execute debugging commands in order to diagnose a problem even before a local technician needed to be dispatched. In theory, the time to diagnose was reduced drastically and the time to replace (assuming the remote diagnosis was accurate) a failed component was shortened. In practice, there were many system level failures that could not be easily detected, due the limited visibility the panel provided. For example, power supplies were not monitored and could only be diagnosed locally. So it was a mixed bag. In addition, spare modules were notoriously unreliable, often with recycled "no trouble found" intermittent issues.
The mid-1970s PDP-11/34 (and later the 11/60) minicomputers introduced a minimalist octal keypad and 7-segment LED front panel. The smaller PDP-11/04 eliminated a panel altogether except power, halt, and boot switches. All low level operations were carried out from the console terminal using ODT commands.
Later on, with the introduction of the DEC VAX 11/780, the ability to diagnose remotely became much more sophisticated, and the VAX was designed from the ground up to not have any external indicators. The console subsystem was an entire PDP-11/03 LSI based minicomputer (itself faceless) housed inside the main CPU cabinet with dual floppy disks. The PDP-11/03 was responsible for loading the machine's microcode on boot. The main CPU had features such as an internal "visibility bus" which could be examined by the console to grab detailed status of internal data paths not normally exposed and the power supplies were monitored. Since the PDP-11/03 was a complete stand alone computer, it could help run diagnostics with even a total failure of the main CPU.
[One notable holdout to the trend away from blinkinlights was the massively parallel Thinking Machines Connection Machine developed in the 1980s. It had thousands of blinking LEDs. Each LED was connected to a single compute element. It was straight out of a science fiction movie.]
I hope this brief explanation makes some sense to the current generation of computer nerds and aids in the understanding of the retro craze.