If your images are too large, you worry they will be stolen. If your images are too small, they lose their impact. Here is what I believe to be the best balance for this problem.
Points of View
There are several points of view on that matter. All of them have their valid arguments and yet each opinion contradicts the others to a certain extent.
This group consists mainly of photographers who are afraid of giving away extra pixels, because of people who do web search for "free large images." In the best case those seekers may credit it with "Source: Google."
Those are the people who are not always photographers, but think images sizes have to be big enough, so they fit on all kinds of screens and resolutions even in the next four years. That group thinks free-image seekers are just a conspiracy theory.
The Pixel Peeper
Most probably, these are fellow photographers. They usually complain they can't determine if you used frequency separation or the good ol' dodge and burn on a full-length-twenty-person group shot. To please those people you should either upload high-resolution images or probably have a loupe tool in your portfolio just as retail product websites have.
The Multiple-Big-Screen Geek
That's the typical geek with several huge monitors, each 5K, and the text is bearably readable, because they don't care about words. They only care about visuals. Big visuals. Your website will probably look like a post card on their screens and they will complain about it.
The Mobile Device Junkie
That group is fine with any website as long as there are good-looking images. They are more than 50% of the traffic on the internet, have sub-2K screens, and are not really impressed about the fact your video is published in 4K.
Finding the Balance
We've got different displays that are expected to render images that are large enough to enjoy them. If we talk only from that perspective we should agree with those with the biggest screens that images have to be uploaded in larger sizes in order to fill up those monitors.
What Displays Do the Viewers Use?
As I said, most of the traffic on the internet is from mobile devices. Those that have more than 4K displays are less than 1%, according to a recent Fstoppers.com statistics report.
The issue with big images is not just the size that can be enjoyed. It has to be balanced with the traffic they generate and with the load time, because today people want everything here, now, and at that very moment.
Text Size Consideration
Big screens are not made for reading text from side to side. Big screens are made for having more area for your applications and screens. Have you ever wondered why most news websites' content is about 1000 pixels in width? If you try to read lines that are long without breaking you won't be able to follow the next line easily.
When you browse a website, it's usually text and images. Do you remember those times when websites with a font size of 12 pixels looked normal? Today 14 pixels is considered a bit small. If you see old websites from 10-15 years ago, their text will look quite small to you. I am saying that with the growth of screen resolution there is a certain limitation because of the text on the screen. Too small the number of pixels will make the text almost unreadable, but you will be able to see images in their full glory.
If the monitor was only a device for images, I would agree that all photographers have to adapt to that and display images as big as they can and dare. But knowing the screens are used for both text and graphics I think there has to be a fair line that an image doesn't have to be more than 1600 pixels to be evaluated, to generate a moderate traffic, and to allow having a quick and responsive website. I'd not upload images more than 1200 pixels, to be honest. On my website I'm still in the sub-1000 range. After all I think it's you and the clients who need to have access to the high-resolution images, not the average viewer on the internet. The potential client can evaluate your work even on small thumbnails. The rest is just a caprice.