I've never had problems connecting Windows laptops to projectors. The only difficulty was that the owner often doesn't know how to switch the display output between the laptop screen, external display, or both. It's easy enough to show them when I'm there, but trying to explain it over the phone can be a nightmare with some users. It's usually Fn+hotkey, and unfortunately different for every laptop. The icon for the function can differ too depending on laptop model, so it's difficult to instruct people over the phone what to look for. The only PC laptop I've had problems with was an old Thinkpad, where Lenovo's display mode auto-switching software kept fighting with Windows' built-in display-mode switching.
The Macbooks have always been more problematic because they come with mini-displayport output. Almost no projector has Displayport input, so you have to have the correct adapter to convert the Macbook's video output to whatever the projector takes (VGA or HDMI usually). Most Mac users don't know this and so don't have this adapter. The better hotels and conference centers have the adapter (or cable which functions as an adapter) for use with their projectors, and veteran presenters with Macs own the adapter. But numerous times I've had to help newbie presenters with a Mac transfer their presentation over to a PC laptop because they had no way to connect their Macbook to the projector.
Let me clarify after reading Solandri's response: after I start up the laptop, I plug that adapter into the mini display port on the laptop, then I plug the other end into the projector (fairly new Viewsonic projector.).
Once the connections are done, I turn on the projector and after it gets warmed up, it finds the connection/laptop and.....voila! What is on my wife's laptop is now being shown from the projector. The image on the laptop shrinks a bit, there is now a black border, maybe 1/2" thick around the outside edge of the laptops display, but you don't see the black border when viewing the projector but we still can see and operate from the laptops display.
I make no changes in the display section of the laptop settings or anywhere else, the projector finds it!
But like Solandri said, sometimes getting the projector and the laptop to see each other can be difficult depending on what make/model laptop you are using.
It took me awhile to figure out that the mini display port was what I needed. The Dell laptop has a HDMI port and the mini display port.
The HDMI port wouldn't work, no matter what I tried for adapters. I called Viewsonic to get help and that was a wasted phone call.
I search Google for hours before I came across that Amazon part I listed above, not knowing if that would work but I ordered it anyway. Many reviewers gave it high marks and mentioned having the same problem as I was having.
My wife teaches class on the weekends, early childhood development, to college students and this was a great addition.
I forgot about the new MBP that require lots of extra adapters. Those Pre-2016 MacBook Pro did not have issues with projectors but I saw many people had issues with Windows laptops at conferences or when they presented their work at universities. The post-2016 MacBook Pro are probably not as good as the previous ones due to issues you mentioned.