You can use a pen display like a regular monitor. However, there are a few things you should be aware of.
It's completely safe. It's safe for your pen display, your computers, and the cables connecting them.
The VAST majority of pen displays use LCD display panels. Just like any monitor or TV that uses LCD panels you can just keep them on all the time.
I've used multiple pen displays as a second display and leave them on 24/7 and my computers are set to never sleep so they are always showing something.
With some LCD panels, If they are showing the same thing on the screen that you many encounter a phenomena called Image Persistence. This is normal and is not a permanent change and is not screen burn in (https://en.wikipedia.org/wiki/Screen_burn-in).
Specific pen displays I have used this way (each has been continuously turned on and showing something for several months at least):
Wacom Cintiq Pro 16 DTH-167
Wacom Cintiq Pro 27 DTH-271
XP-Pen Artist Pro 16 GEN2 MD160QH
Wacom One GEN1 (DTC-133)
Wacom One 13 GEN2 (DTH-134)
Wacom One 12 GEN2 (DTC-121)
Huion Kamvas 22 Plus (GS2202)
Huion Kamvas 13 (GS1331)
Huion Kamvas Pro 16 Plus 4k (GT1562)
Huion Kamvas Pro 24 4K (GT2401)
Xencelabs Pen Display 24 (LPH2412U-A)
OLED panels are relatively new to pen displays. They only started appearing in 2024 with the arrival of the Wacom Movink. How long OLED panels can last without issues like burn-in is unknown, but it is widely understood that their lifetime is less than that of an IPS panel. For now, my recommendation is to turn off OLED pen displays if you are not actively using them.
Pen displays typically they only up to 60Hz. Higher refresh rates are EXTREMELY rare. More here: Pen display refresh rate
A monitor often has a variety of inputs. For example, most of the monitors I have support these display inputs such as HDMI, DisplayPort, USB-C.
Some pen displays have a variety of inputs. The Wacom Cintiq pro 27 DTH271 is a great example of one. It supports all of the inputs mentioned above.
But most modern pen displays now have only USB-C ports - usually two. One for a display signal & data and one for additional power if needed.
Typically monitors have to aspect ratios: 16:9 and 16:10. And there are variety of widescreen or ultra-widescreen monitors that support many other aspect ratios.
Pen displays have much less diversity of aspect ratios. The vast majority of modern pen displays are exactly 16:9. A very small number are 16:10.
Learn more: active area aspect ratio
Monitors and pen displays use various panel tech such as:
IPS
TN
VA
OLED
OLED introduction to pen displays. Starting by around May 2024, we seen the introduction of a few pen displays with OLED panels. The first pen display to use OLED was the Wacom Movink 13 (DTH-135) and the second OLED pen display was the Xencelabs Pen Display 16.
Pen displays aren't especially bright. most around around 250 nits. And only a few are >= 300 nits.
More here: Brightness
Most often monitors support VESA mounting so you can attach them to a stand or an arm.
Many pen displays support VESA mounting also. However, the pen displays that are 16" or smaller often do not support VESA mounting. Likely they do not support VESA mounting because these sizes of pen displays are to thin to do so.
More here:
Monitors tend to have the normal power cables and adapters.
Modern pen displays may also use normal power adapters. But some support getting power via their USB-C ports.
It varies quite a bit among pen displays, but often they exhibit more Anti-Glare sparkle than monitors. Sometimes it is quite noticeable. Some people are very irritated by the visual effect of this anti-glare sparkle. More here: Anti-glare sparkle
Many monitors come with built-in speakers. They usually sound terrible, but they can be useful. As far as I am aware, no pen displays have speakers.
One of the benefits of supporting multiple display input ports is that it makes it possible to display two or more inputs simultaneously. Many monitors allow this now and it is very useful for very wide monitors. Pen displays do not support this feature.
It's common question whether pen displays would get to hot if they are continually used. Pen displays don't get any hotter than a normal monitor. More here: Heat
Monitors are almost always completely silent and don't even have fans. However, some pen displays - notably some Wacom Cintiq Pro models - have fans are are known for fan noise. If you are sensitive to noise research this first.