Gathering references is a slow job made of fast steps. Right click, save image, pick a folder, rename it so you can find it, go back for the next one. Twenty minutes later you have a folder of downloads and a canvas that is still empty.
The copying part was never the problem. The problem is that a normal clipboard forgets everything except the last one, so saving files is the only way to keep them.
The shorter version
Copy as you browse. Just copy.
Every image you copy is kept and filed as an image, so at the end of the browse you have all of them, in order, waiting. Then you select the ones you want and paste once. They land as a laid out board instead of a pile you have to arrange.
Why copying beats saving
A saved file makes you name it before you know if you want it. That is a decision, and you make it twenty times in a row while you are trying to think about something else.
Copying makes no decision. You keep everything, pick later, and never touch Finder.
Colours come along too
A mood board is rarely only images. Copy a hex code from a site and it is filed as a colour, with a swatch, so the palette is sitting beside the pictures rather than buried in a notes file.
If a set of references belongs together, drop them onto a pinboard as you collect them, so a week of research stays one thing instead of fifty scattered items.
Try it on the next thing you are gathering
Nothing to set up. Copy, copy, copy, then select and paste.